Refactor and extract shared request handler logic from supervisor _handle_request methods

[leeyspaul]

Extract shared request handling into request_handlers.py and reuse it in the task supervisor, triggerer, and DAG file processor.

This reduces duplicated _handle_request() logic across the subprocess supervisors and aligns GetXCom handling on the same response-normalization path.

Related: #65570

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Note:

No new tests here because this was intended as a behavior-preserving refactor and the affected handler paths already have existing supervisor/processor coverage.

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[leeyspaul]

This branch is currently based on #65269 for the shared request_handlers.py structure. Once that PR merges, I’ll rebase this branch onto main.

[leeyspaul]

This PR is currently waiting on #65269 to merge, and then we'll mark this as ready afterwards.

@ferruzzi two things below that I'd like to ask for your attention on!

1. Please see the comment about the self.id for GetPrevSuccessfulDagRun here: Refactor and extract shared request handler logic from supervisor _handle_request methods #65624 (comment)
2. I left the GetConnection and GetVariable alone in DFP as there was not an exact match with the helper (added masking secrets), I do agree that I think it should be included and probably changed. I figure if that's the case it might be another good first issue to contribute back to the community :).

[ferruzzi]

Personally I think DFP should have masked GetConnection and GetVariable and I would personally call this a bugfix (and a security violation fix...) but maybe message #contributors in Slack to see if there are any obvious reasons not to?

[leeyspaul]

Personally I think DFP should have masked GetConnection and GetVariable and I would personally call this a bugfix (and a security violation fix...) but maybe message #contributors in Slack to see if there are any obvious reasons not to?

Will do, I'll ask in Slack. Thank you.

Slack thread here: https://apache-airflow.slack.com/archives/C06K9Q5G2UA/p1776817558532799

[ferruzzi]

Had a chat with @o-nikolas and @vincbeck this morning, their recommendation is to add the mask, but do it in its own PR so we can backport that one.

[leeyspaul]

Had a chat with @o-nikolas and @vincbeck this morning, their recommendation is to add the mask, but do it in its own PR so we can backport that one.

That sounds good, I'll open up a separate PR for that one.

[leeyspaul]

Whoops, sorry, still pending merge of #65269. Converted back to draft.

[ferruzzi]

#65269 is merged and I think this looks good. We should be ready to merge it, I think??