Remove unused legacy action logging helper

[aaron-y-chen]

Hi team, I think this is dead code.

action_logger.py seems to have been created in #24079, and #47171 deleted the last two callers (connection_endpoint.py and variable_endpoint.py).

I searched the whole repository and couldn't find any remaining usages.

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[github-actions]

Backport successfully created: v3-3-test

Note: As of Merging PRs targeted for Airflow 3.X
the committer who merges the PR is responsible for backporting the PRs that are bug fixes (generally speaking) to the maintenance branches.

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Status	Branch	Result
✅	v3-3-test