Better error handling for running ti heartbeats after task is cleared

[kriti-sc]

Return 410 - GONE instead of 404 - NOT_FOUND when the running task instance heartbeats after task is cleared.

When a running task is cleared, the previous task instance is moved from the Task Instance table to the Task Instance History table. As a result, if the task instance hearbeats, the api server returns a 404. A more appropriate error is 410.

closes: #53140

Airflow task logs:

Scheduler and API server logs:

api-server | [2025-10-06T21:28:42.135650Z] {task_instances.py:608} ERROR - Task Instance not found in Task Instance table, might have moved to the Task Instance History table ti_id=0199bb6c-f0be-7686-a26e-30f70d893ae1
api-server | INFO:     127.0.0.1:53520 - "PUT /execution/task-instances/0199bb6c-f0be-7686-a26e-30f70d893ae1/heartbeat HTTP/1.1" 410 Gone
scheduler  | [2025-10-06T21:28:42.137967Z] {supervisor.py:1103} ERROR - Server indicated the task shouldn't be running anymore detail={'detail': {'reason': 'not_found', 'message': 'Task Instance not found, might have moved to the Task Instance History table'}} status_code=410 ti_id=UUID('0199bb6c-f0be-7686-a26e-30f70d893ae1')
scheduler  | [2025-10-06T21:28:42.144732Z] {supervisor.py:713} INFO - Process exited pid=96561 exit_code=0 signal_sent=SIGTERM
scheduler  | [2025-10-06T21:28:42.144989Z] {supervisor.py:1899} INFO - Task finished exit_code=0 duration=15.431881000055 final_state=SERVER_TERMINATED

---

^ Add meaningful description above
Read the Pull Request Guidelines for more information.
In case of fundamental code changes, an Airflow Improvement Proposal (AIP) is needed.
In case of a new dependency, check compliance with the ASF 3rd Party License Policy.
In case of backwards incompatible changes please leave a note in a newsfragment file, named {pr_number}.significant.rst or {issue_number}.significant.rst, in airflow-core/newsfragments.

[boring-cyborg]

Congratulations on your first Pull Request and welcome to the Apache Airflow community! If you have any issues or are unsure about any anything please check our Contributors' Guide (https://github.com/apache/airflow/blob/main/contributing-docs/README.rst)
Here are some useful points:

• Pay attention to the quality of your code (ruff, mypy and type annotations). Our prek-hooks will help you with that.
• In case of a new feature add useful documentation (in docstrings or in docs/ directory). Adding a new operator? Check this short guide Consider adding an example DAG that shows how users should use it.
• Consider using Breeze environment for testing locally, it's a heavy docker but it ships with a working Airflow and a lot of integrations.
• Be patient and persistent. It might take some time to get a review or get the final approval from Committers.
• Please follow ASF Code of Conduct for all communication including (but not limited to) comments on Pull Requests, Mailing list and Slack.
• Be sure to read the Airflow Coding style.
• Always keep your Pull Requests rebased, otherwise your build might fail due to changes not related to your commits.
  Apache Airflow is a community-driven project and together we are making it better 🚀.
  In case of doubts contact the developers at:
  Mailing List: [email protected]
  Slack: https://s.apache.org/airflow-slack

[uranusjr]

I think 404 should still exist, there’s a difference between a ti that never existed and a ti that existed but is gone.

[amoghrajesh]

I think these changes are insufficient, look at my comments

[amoghrajesh]

This is added here by mistake?

[amoghrajesh]

I think we should actually validate that, check if it is present in the TIH table.

Two situations possible here:

1. Task Instance doesnt exist and not in TIH table -> return 404
2. Task Instance doesnt exist and present in TIH table -> return 410

[amoghrajesh]

Formatting looks off -- static checks will fail