Add dependency to the running_deps

[avkirilishin]

closes: #20461

Problem: Airflow is trying to schedule tasks prior to DAG's start_date.
Solution: Added ExecDateAfterStartDateDep to the dependencies that need to be met for a given task instance to be set to 'RUNNING' state.

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[ephraimbuddy]

I don't think this is the right fix. If I understand correctly, the problem is that the scheduler is creating dagruns for those past dates and not that the task instances are being scheduled. The ExecDateAfterStartDateDep currently in place will prevent tasks from getting into queued state if the start date is before the execution date

[avkirilishin]

I don't think this is the right fix. If I understand correctly, the problem is that the scheduler is creating dagruns for those past dates and not that the task instances are being scheduled. The ExecDateAfterStartDateDep currently in place will prevent tasks from getting into queued state if the start date is before the execution date

I explained it here: #20461 (comment)

I think there are two different problems:

The problem is related to the different logic of the scheduler before and after the update. Maybe there are no tasks in the running dags or something else. Can you show the rows for this dag run in dag, dag_run and task_instance?

I agree with you that it is not the right behavior for the scheduler to continue scheduling runs that are earlier than the actual start date of the DAG or Task. It can happen, for example, after turning the dag off and back on. So I made a PR to fix it: #21684

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