Removes AIP-44 from dag processing manager and internal_api_call

[potiuk]

This is the last "internal_api_call" change from AIP-44 removal and it not only removes the dag_processsing/manager calls but also the internal_api_call itself.

Part of #44436

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[potiuk]

cc: @jason810496

[jscheffl]

Wohoo, house is clean!

[jscheffl]

...ah wheres still some cleaning and removal in airflow/serialization/pydantic/** is needed as well?
Will airflow/serialization/** actually also be removed or will this stay? (I assume we don't need this with the old API, correct?)

[potiuk]

...ah wheres still some cleaning and removal in airflow/serialization/pydantic/** is needed as well?
Will airflow/serialization/** actually also be removed or will this stay? (I assume we don't need this with the old API, correct?)

Yep. there is one more step in #44436 - remove all *Pydantic classes aand that's part of it. One problem there is that Pydantic classes are currently used as a way to serialize Context for PythonVirtualenvOperator and ExternalPythonOperator - so we cannot remove them "as-is" - we have to provide a replacement - which is likely tied to the Task SDK API changes - cc: @ashb @kaxil