diff --git a/airflow-core/docs/img/airflow_erd.sha256 b/airflow-core/docs/img/airflow_erd.sha256
index 9a2b4388439c0..a76243f9c41cb 100644
--- a/airflow-core/docs/img/airflow_erd.sha256
+++ b/airflow-core/docs/img/airflow_erd.sha256
@@ -1 +1 @@
-4a44b71c7fe18f8f7c60ac1d576d29c618ee370f810fe1bb8a1894a3d77fcb0d
\ No newline at end of file
+f5a99cb756403f20d63b7a4d0df67f776ac43d53d9bcc75323c4b80044d409e4
\ No newline at end of file
diff --git a/airflow-core/src/airflow/migrations/versions/0042_3_0_0_add_uuid_primary_key_to_task_instance_.py b/airflow-core/src/airflow/migrations/versions/0042_3_0_0_add_uuid_primary_key_to_task_instance_.py
index ccd0697ff63ab..df7965d38e934 100644
--- a/airflow-core/src/airflow/migrations/versions/0042_3_0_0_add_uuid_primary_key_to_task_instance_.py
+++ b/airflow-core/src/airflow/migrations/versions/0042_3_0_0_add_uuid_primary_key_to_task_instance_.py
@@ -206,7 +206,10 @@ def upgrade():
         op.execute(pg_uuid7_fn)
 
         # Migrate existing rows with UUID v7 using a timestamp-based generation
+        batch_num = 0
         while True:
+            batch_num += 1
+            print(f"processing batch {batch_num}")
             result = conn.execute(
                 text(
                     """
diff --git a/airflow-core/src/airflow/migrations/versions/0049_3_0_0_remove_pickled_data_from_xcom_table.py b/airflow-core/src/airflow/migrations/versions/0049_3_0_0_remove_pickled_data_from_xcom_table.py
index c3972edbd12ab..fed378378290a 100644
--- a/airflow-core/src/airflow/migrations/versions/0049_3_0_0_remove_pickled_data_from_xcom_table.py
+++ b/airflow-core/src/airflow/migrations/versions/0049_3_0_0_remove_pickled_data_from_xcom_table.py
@@ -28,7 +28,7 @@
 from __future__ import annotations
 
 import sqlalchemy as sa
-from alembic import op
+from alembic import context, op
 from sqlalchemy import text
 from sqlalchemy.dialects.mysql import LONGBLOB
 
@@ -77,9 +77,24 @@ def upgrade():
     condition = condition_templates.get(dialect)
     if not condition:
         raise RuntimeError(f"Unsupported dialect: {dialect}")
-
     # Key is a reserved keyword in MySQL, so we need to quote it
     quoted_key = conn.dialect.identifier_preparer.quote("key")
+    if dialect == "postgresql" and not context.is_offline_mode():
+        curr_timeout = (
+            int(
+                conn.execute(
+                    text("""
+                        SELECT setting
+                        FROM pg_settings
+                        WHERE name = 'statement_timeout'
+                    """)
+                ).scalar_one()
+            )
+            / 1000
+        )
+        if curr_timeout > 0 and curr_timeout < 1800:
+            print("setting local statement timeout to 1800s")
+            conn.execute(text("SET LOCAL statement_timeout='1800s'"))
 
     # Archive pickled data using the condition
     conn.execute(
diff --git a/airflow-core/src/airflow/migrations/versions/0055_3_0_0_remove_pickled_data_from_dagrun_table.py b/airflow-core/src/airflow/migrations/versions/0055_3_0_0_remove_pickled_data_from_dagrun_table.py
index 07d012ddf5719..31b71e2bedc3b 100644
--- a/airflow-core/src/airflow/migrations/versions/0055_3_0_0_remove_pickled_data_from_dagrun_table.py
+++ b/airflow-core/src/airflow/migrations/versions/0055_3_0_0_remove_pickled_data_from_dagrun_table.py
@@ -47,6 +47,17 @@
 def upgrade():
     """Apply remove pickled data from dagrun table."""
     conn = op.get_bind()
+    empty_vals = {
+        "mysql": "X'80057D942E'",
+        "postgresql": r"'\x80057D942E'",
+        "sqlite": "X'80057D942E'",
+    }
+    dialect = conn.dialect.name
+    try:
+        empty_val = empty_vals[dialect]
+    except KeyError:
+        raise RuntimeError(f"Dialect {dialect} not supported.")
+
     conf_type = sa.JSON().with_variant(postgresql.JSONB, "postgresql")
     op.add_column("dag_run", sa.Column("conf_json", conf_type, nullable=True))
 
@@ -61,12 +72,20 @@ def upgrade():
             """)
         )
     else:
-        BATCH_SIZE = 100
+        BATCH_SIZE = 1000
         offset = 0
         while True:
+            err_count = 0
+            batch_num = offset + 1
+            print(f"converting dag run conf. batch={batch_num}")
             rows = conn.execute(
                 text(
-                    f"SELECT id,conf FROM dag_run WHERE conf IS not NULL order by id LIMIT {BATCH_SIZE} OFFSET {offset}"
+                    "SELECT id, conf "
+                    "FROM dag_run "
+                    "WHERE conf IS not NULL "
+                    f"AND conf != {empty_val}"
+                    f"ORDER BY id LIMIT {BATCH_SIZE} "
+                    f"OFFSET {offset}"
                 )
             ).fetchall()
             if not rows:
@@ -85,9 +104,11 @@ def upgrade():
                                             """),
                         {"json_data": json_data, "id": row_id},
                     )
-                except Exception as e:
-                    print(f"Error converting dagrun conf to json for dagrun ID {row_id}: {e}")
+                except Exception:
+                    err_count += 1
                     continue
+            if err_count:
+                print(f"could not convert dag run conf for {err_count} records. batch={batch_num}")
             offset += BATCH_SIZE
 
     op.drop_column("dag_run", "conf")
@@ -112,12 +133,16 @@ def downgrade():
         )
 
     else:
-        BATCH_SIZE = 100
+        BATCH_SIZE = 1000
         offset = 0
         while True:
             rows = conn.execute(
                 text(
-                    f"SELECT id,conf FROM dag_run WHERE conf IS not NULL order by id LIMIT {BATCH_SIZE} OFFSET {offset}"
+                    "SELECT id,conf "
+                    "FROM dag_run "
+                    "WHERE conf IS NOT NULL "
+                    f"ORDER BY id LIMIT {BATCH_SIZE} "
+                    f"OFFSET {offset}"
                 )
             ).fetchall()
             if not rows: