Get LatestOnlyOperator working with Task SDK

[kaxil]

closes #48897

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[jscheffl]

I attempted to refresh screenshots for http://apache-airflow-docs.s3-website.eu-central-1.amazonaws.com/docs/apache-airflow/stable/core-concepts/dags.html in context of #45649 ... and attempted to create a new shot for /img/latest_only_with_trigger.png and failed making the example latest_only_with_trigger working to re-create the screenshot. Either I was too stupid or it was too late in the night... or the LatestOnlyOperator is broken? Too lazy to file a bug report... but can @kaxil you briefly check if the example DAG is working as expected on your side? I was testing 3.0.0rc4

Logs:

[2025-04-22, 00:02:35] INFO - DAG bundles loaded: dags-folder, example_dags: source="airflow.dag_processing.bundles.manager.DagBundlesManager"
[2025-04-22, 00:02:35] INFO - Filling up the DagBag from /opt/airflow/airflow-core/src/airflow/example_dags/example_latest_only_with_trigger.py: source="airflow.models.dagbag.DagBag"
[2025-04-22, 00:02:35] INFO - Checking latest only with left_window: 2025-04-06 04:00:00+00:00 right_window: 2025-04-06 04:00:00+00:00 now: 2025-04-21 22:02:35.447824+00:00: source="airflow.task.operators.airflow.providers.standard.operators.latest_only.LatestOnlyOperator"
[2025-04-22, 00:02:35] INFO - Zero-length interval [2025-04-06 04:00:00+00:00, 2025-04-06 04:00:00+00:00) from timetable (<class 'airflow.timetables.trigger.DeltaTriggerTimetable'>); treating current run as latest.: source="airflow.task.operators.airflow.providers.standard.operators.latest_only.LatestOnlyOperator"
[2025-04-22, 00:02:35] INFO - Branch into ['task1']: source="airflow.task.operators.airflow.providers.standard.operators.latest_only.LatestOnlyOperator"
[2025-04-22, 00:02:35] INFO - Following branch {'task1'}: source="airflow.task.operators.airflow.providers.standard.operators.latest_only.LatestOnlyOperator"
[2025-04-22, 00:02:35] INFO - Skipping tasks []: source="airflow.task.operators.airflow.providers.standard.operators.latest_only.LatestOnlyOperator"
[2025-04-22, 00:02:35] INFO - Pushing xcom: ti="RuntimeTaskInstance(id=UUID('01965a5f-e162-7035-90c0-23f7bf0567c2'), task_id='latest_only', dag_id='latest_only_with_trigger', run_id='scheduled__2025-04-06T00:00:00+00:00', try_number=1, map_index=-1, hostname='a8cfc25a576e', context_carrier=None, task=<Task(LatestOnlyOperator): latest_only>, bundle_instance=LocalDagBundle(name=example_dags), max_tries=0, start_date=datetime.datetime(2025, 4, 21, 22, 2, 35, 333350, tzinfo=TzInfo(UTC)), end_date=None, is_mapped=False)": source="task"
[2025-04-22, 00:02:35] INFO - Task instance is in running state: chan="stdout": source="task"
[2025-04-22, 00:02:35] INFO -  Previous state of the Task instance: queued: chan="stdout": source="task"
[2025-04-22, 00:02:35] INFO - Current task name:latest_only: chan="stdout": source="task"
[2025-04-22, 00:02:35] INFO - Dag name:latest_only_with_trigger: chan="stdout": source="task"
[2025-04-22, 00:02:35] INFO - Task instance in success state: chan="stdout": source="task"
[2025-04-22, 00:02:35] INFO -  Previous state of the Task instance: running: chan="stdout": source="task"
[2025-04-22, 00:02:35] INFO - Task operator:<Task(LatestOnlyOperator): latest_only>: chan="stdout": source="task"