diff --git a/providers/standard/src/airflow/providers/standard/operators/bash.py b/providers/standard/src/airflow/providers/standard/operators/bash.py
index caee52072e10e..e10192a05b228 100644
--- a/providers/standard/src/airflow/providers/standard/operators/bash.py
+++ b/providers/standard/src/airflow/providers/standard/operators/bash.py
@@ -26,12 +26,7 @@
 
 from airflow.exceptions import AirflowException, AirflowSkipException
 from airflow.providers.standard.hooks.subprocess import SubprocessHook, SubprocessResult, working_directory
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, AIRFLOW_V_3_1_PLUS
-
-if AIRFLOW_V_3_1_PLUS:
-    from airflow.sdk import BaseOperator
-else:
-    from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, BaseOperator
 
 if AIRFLOW_V_3_0_PLUS:
     from airflow.sdk.execution_time.context import context_to_airflow_vars
diff --git a/providers/standard/src/airflow/providers/standard/operators/branch.py b/providers/standard/src/airflow/providers/standard/operators/branch.py
index 064bb52afe188..98c059ac38eac 100644
--- a/providers/standard/src/airflow/providers/standard/operators/branch.py
+++ b/providers/standard/src/airflow/providers/standard/operators/branch.py
@@ -22,12 +22,7 @@
 from collections.abc import Iterable
 from typing import TYPE_CHECKING
 
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, AIRFLOW_V_3_1_PLUS
-
-if AIRFLOW_V_3_1_PLUS:
-    from airflow.sdk import BaseOperator
-else:
-    from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, BaseOperator
 
 if AIRFLOW_V_3_0_PLUS:
     from airflow.providers.standard.utils.skipmixin import SkipMixin
diff --git a/providers/standard/src/airflow/providers/standard/operators/empty.py b/providers/standard/src/airflow/providers/standard/operators/empty.py
index cdfebf3a4139c..b9a480bc86ea9 100644
--- a/providers/standard/src/airflow/providers/standard/operators/empty.py
+++ b/providers/standard/src/airflow/providers/standard/operators/empty.py
@@ -18,12 +18,7 @@
 
 from typing import TYPE_CHECKING
 
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_1_PLUS
-
-if AIRFLOW_V_3_1_PLUS:
-    from airflow.sdk import BaseOperator
-else:
-    from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import BaseOperator
 
 if TYPE_CHECKING:
     from airflow.sdk.definitions.context import Context
diff --git a/providers/standard/src/airflow/providers/standard/operators/python.py b/providers/standard/src/airflow/providers/standard/operators/python.py
index 92387d28cbffd..f6efcf3bf0d26 100644
--- a/providers/standard/src/airflow/providers/standard/operators/python.py
+++ b/providers/standard/src/airflow/providers/standard/operators/python.py
@@ -50,18 +50,13 @@
 )
 from airflow.models.variable import Variable
 from airflow.providers.standard.utils.python_virtualenv import prepare_virtualenv, write_python_script
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, AIRFLOW_V_3_1_PLUS
+from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, BaseOperator
 from airflow.utils import hashlib_wrapper
 from airflow.utils.context import context_copy_partial, context_merge
 from airflow.utils.file import get_unique_dag_module_name
 from airflow.utils.operator_helpers import KeywordParameters
 from airflow.utils.process_utils import execute_in_subprocess
 
-if AIRFLOW_V_3_1_PLUS:
-    from airflow.sdk import BaseOperator
-else:
-    from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
-
 if AIRFLOW_V_3_0_PLUS:
     from airflow.providers.standard.operators.branch import BaseBranchOperator
     from airflow.providers.standard.utils.skipmixin import SkipMixin
diff --git a/providers/standard/src/airflow/providers/standard/operators/smooth.py b/providers/standard/src/airflow/providers/standard/operators/smooth.py
index 6799e07a5ef05..9b3d1ff181e26 100644
--- a/providers/standard/src/airflow/providers/standard/operators/smooth.py
+++ b/providers/standard/src/airflow/providers/standard/operators/smooth.py
@@ -19,12 +19,7 @@
 
 from typing import TYPE_CHECKING
 
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
-
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk import BaseOperator
-else:
-    from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import BaseOperator
 
 if TYPE_CHECKING:
     from airflow.sdk.definitions.context import Context
diff --git a/providers/standard/src/airflow/providers/standard/operators/trigger_dagrun.py b/providers/standard/src/airflow/providers/standard/operators/trigger_dagrun.py
index 4f474c3e6996e..998fd4c8d7e55 100644
--- a/providers/standard/src/airflow/providers/standard/operators/trigger_dagrun.py
+++ b/providers/standard/src/airflow/providers/standard/operators/trigger_dagrun.py
@@ -34,12 +34,11 @@
     DagNotFound,
     DagRunAlreadyExists,
 )
-from airflow.models import BaseOperator
 from airflow.models.dag import DagModel
 from airflow.models.dagbag import DagBag
 from airflow.models.dagrun import DagRun
 from airflow.providers.standard.triggers.external_task import DagStateTrigger
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
+from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, BaseOperator, BaseOperatorLink
 from airflow.utils import timezone
 from airflow.utils.state import DagRunState
 from airflow.utils.types import NOTSET, ArgNotSet, DagRunType
@@ -60,11 +59,9 @@
         from airflow.utils.context import Context
 
 if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk import BaseOperatorLink
     from airflow.sdk.execution_time.xcom import XCom
 else:
     from airflow.models import XCom  # type: ignore[no-redef]
-    from airflow.models.baseoperatorlink import BaseOperatorLink  # type: ignore[no-redef]
 
 
 class DagIsPaused(AirflowException):
diff --git a/providers/standard/src/airflow/providers/standard/sensors/bash.py b/providers/standard/src/airflow/providers/standard/sensors/bash.py
index 5e8dd0b24650f..9b83b4af187a3 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/bash.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/bash.py
@@ -24,12 +24,7 @@
 from typing import TYPE_CHECKING
 
 from airflow.exceptions import AirflowFailException
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
-
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import BaseSensorOperator
 
 if TYPE_CHECKING:
     try:
diff --git a/providers/standard/src/airflow/providers/standard/sensors/date_time.py b/providers/standard/src/airflow/providers/standard/sensors/date_time.py
index a2e2478109f59..85758210a05f6 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/date_time.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/date_time.py
@@ -23,14 +23,9 @@
 from typing import TYPE_CHECKING, Any, NoReturn
 
 from airflow.providers.standard.triggers.temporal import DateTimeTrigger
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
+from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, BaseSensorOperator
 from airflow.utils import timezone
 
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type: ignore[no-redef]
-
 try:
     from airflow.triggers.base import StartTriggerArgs
 except ImportError:
diff --git a/providers/standard/src/airflow/providers/standard/sensors/external_task.py b/providers/standard/src/airflow/providers/standard/sensors/external_task.py
index 974608bf714f4..32ad0111295bd 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/external_task.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/external_task.py
@@ -39,14 +39,16 @@
 from airflow.providers.standard.operators.empty import EmptyOperator
 from airflow.providers.standard.triggers.external_task import WorkflowTrigger
 from airflow.providers.standard.utils.sensor_helper import _get_count, _get_external_task_group_task_ids
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
+from airflow.providers.standard.version_compat import (
+    AIRFLOW_V_3_0_PLUS,
+    BaseOperator,
+    BaseOperatorLink,
+    BaseSensorOperator,
+)
 from airflow.utils.file import correct_maybe_zipped
 from airflow.utils.state import State, TaskInstanceState
 
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type:ignore[no-redef]
+if not AIRFLOW_V_3_0_PLUS:
     from airflow.utils.session import NEW_SESSION, provide_session
 
 if TYPE_CHECKING:
@@ -55,19 +57,11 @@
     from airflow.models.taskinstancekey import TaskInstanceKey
 
     if AIRFLOW_V_3_0_PLUS:
-        from airflow.sdk import BaseOperator
         from airflow.sdk.definitions.context import Context
     else:
-        from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
         from airflow.utils.context import Context  # type: ignore[no-redef]
 
 
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk import BaseOperatorLink
-else:
-    from airflow.models.baseoperatorlink import BaseOperatorLink  # type: ignore[no-redef]
-
-
 class ExternalDagLink(BaseOperatorLink):
     """
     Operator link for ExternalTaskSensor and ExternalTaskMarker.
diff --git a/providers/standard/src/airflow/providers/standard/sensors/filesystem.py b/providers/standard/src/airflow/providers/standard/sensors/filesystem.py
index 10315dc88a97e..32681cb0f2716 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/filesystem.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/filesystem.py
@@ -29,12 +29,7 @@
 from airflow.exceptions import AirflowException
 from airflow.providers.standard.hooks.filesystem import FSHook
 from airflow.providers.standard.triggers.file import FileTrigger
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
-
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import BaseSensorOperator
 
 try:
     from airflow.triggers.base import StartTriggerArgs
diff --git a/providers/standard/src/airflow/providers/standard/sensors/python.py b/providers/standard/src/airflow/providers/standard/sensors/python.py
index 512ebab4449d3..d6fc454018cc2 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/python.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/python.py
@@ -20,15 +20,10 @@
 from collections.abc import Callable, Mapping, Sequence
 from typing import TYPE_CHECKING, Any
 
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
+from airflow.providers.standard.version_compat import BaseSensorOperator, PokeReturnValue
 from airflow.utils.context import context_merge
 from airflow.utils.operator_helpers import determine_kwargs
 
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator, PokeReturnValue
-else:
-    from airflow.sensors.base import BaseSensorOperator, PokeReturnValue  # type: ignore[no-redef]
-
 if TYPE_CHECKING:
     try:
         from airflow.sdk.definitions.context import Context
diff --git a/providers/standard/src/airflow/providers/standard/sensors/time.py b/providers/standard/src/airflow/providers/standard/sensors/time.py
index ad02dc4dc82a9..6d72c29fb4a81 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/time.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/time.py
@@ -25,12 +25,7 @@
 from airflow.configuration import conf
 from airflow.exceptions import AirflowProviderDeprecationWarning
 from airflow.providers.standard.triggers.temporal import DateTimeTrigger
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
-
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type: ignore[no-redef]
+from airflow.providers.standard.version_compat import BaseSensorOperator
 
 try:
     from airflow.triggers.base import StartTriggerArgs
diff --git a/providers/standard/src/airflow/providers/standard/sensors/time_delta.py b/providers/standard/src/airflow/providers/standard/sensors/time_delta.py
index 5b38a2b078e85..492e9aafa1da6 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/time_delta.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/time_delta.py
@@ -28,14 +28,9 @@
 from airflow.configuration import conf
 from airflow.exceptions import AirflowProviderDeprecationWarning, AirflowSkipException
 from airflow.providers.standard.triggers.temporal import DateTimeTrigger, TimeDeltaTrigger
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
+from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS, BaseSensorOperator
 from airflow.utils import timezone
 
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type: ignore[no-redef]
-
 if TYPE_CHECKING:
     try:
         from airflow.sdk.definitions.context import Context
diff --git a/providers/standard/src/airflow/providers/standard/sensors/weekday.py b/providers/standard/src/airflow/providers/standard/sensors/weekday.py
index 6f3af7a318241..ac23e1ac9cb6c 100644
--- a/providers/standard/src/airflow/providers/standard/sensors/weekday.py
+++ b/providers/standard/src/airflow/providers/standard/sensors/weekday.py
@@ -21,14 +21,9 @@
 from typing import TYPE_CHECKING
 
 from airflow.providers.standard.utils.weekday import WeekDay
-from airflow.providers.standard.version_compat import AIRFLOW_V_3_0_PLUS
+from airflow.providers.standard.version_compat import BaseSensorOperator
 from airflow.utils import timezone
 
-if AIRFLOW_V_3_0_PLUS:
-    from airflow.sdk.bases.sensor import BaseSensorOperator
-else:
-    from airflow.sensors.base import BaseSensorOperator  # type: ignore[no-redef]
-
 if TYPE_CHECKING:
     try:
         from airflow.sdk.definitions.context import Context
diff --git a/providers/standard/src/airflow/providers/standard/version_compat.py b/providers/standard/src/airflow/providers/standard/version_compat.py
index 42bdcc7da03df..e630ace142f2b 100644
--- a/providers/standard/src/airflow/providers/standard/version_compat.py
+++ b/providers/standard/src/airflow/providers/standard/version_compat.py
@@ -32,5 +32,29 @@ def get_base_airflow_version_tuple() -> tuple[int, int, int]:
     return airflow_version.major, airflow_version.minor, airflow_version.micro
 
 
-AIRFLOW_V_3_0_PLUS = get_base_airflow_version_tuple() >= (3, 0, 0)
-AIRFLOW_V_3_1_PLUS = get_base_airflow_version_tuple() >= (3, 1, 0)
+AIRFLOW_V_3_0_PLUS: bool = get_base_airflow_version_tuple() >= (3, 0, 0)
+AIRFLOW_V_3_1_PLUS: bool = get_base_airflow_version_tuple() >= (3, 1, 0)
+
+# BaseOperator is not imported from SDK from 3.0 (and only done from 3.1) due to a bug with
+# DecoratedOperator -- where `DecoratedOperator._handle_output` needed `xcom_push` to exist on `BaseOperator`
+# even though it wasn't used.
+if AIRFLOW_V_3_1_PLUS:
+    from airflow.sdk import BaseOperator
+else:
+    from airflow.models.baseoperator import BaseOperator  # type: ignore[no-redef]
+
+if AIRFLOW_V_3_0_PLUS:
+    from airflow.sdk import BaseOperatorLink
+    from airflow.sdk.bases.sensor import BaseSensorOperator, PokeReturnValue
+else:
+    from airflow.models.baseoperatorlink import BaseOperatorLink  # type: ignore[no-redef]
+    from airflow.sensors.base import BaseSensorOperator, PokeReturnValue  # type: ignore[no-redef]
+
+__all__ = [
+    "AIRFLOW_V_3_0_PLUS",
+    "AIRFLOW_V_3_1_PLUS",
+    "BaseOperator",
+    "BaseOperatorLink",
+    "BaseSensorOperator",
+    "PokeReturnValue",
+]
diff --git a/providers/standard/tests/unit/standard/operators/test_trigger_dagrun.py b/providers/standard/tests/unit/standard/operators/test_trigger_dagrun.py
index 190973b477aaa..ad63b23096fb9 100644
--- a/providers/standard/tests/unit/standard/operators/test_trigger_dagrun.py
+++ b/providers/standard/tests/unit/standard/operators/test_trigger_dagrun.py
@@ -182,9 +182,9 @@ def test_trigger_dagrun_operator_templated_invalid_conf(self, dag_maker):
             )
         dag_maker.sync_dagbag_to_db()
         parse_and_sync_to_db(self.f_name)
-        dag_maker.create_dagrun()
+        dr = dag_maker.create_dagrun()
         with pytest.raises(ValueError, match="^conf parameter should be JSON Serializable$"):
-            task.run(start_date=DEFAULT_DATE, end_date=DEFAULT_DATE)
+            dag_maker.run_ti(task.task_id, dr)
 
     def test_trigger_dagrun_with_no_failed_state(self, dag_maker):
         task = TriggerDagRunOperator(