Ensure recorder still shuts down if the final commit fails

[bdraco]

Proposed change

If the final commit in _end_session raised, we would never close the event session which would leave the connection open leading to an unclean shutdown.

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New integration (thank you!)
• New feature (which adds functionality to an existing integration)
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• Breaking change (fix/feature causing existing functionality to break)
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• This PR fixes or closes issue: fixes #
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[home-assistant]

Hey there @home-assistant/core, mind taking a look at this pull request as it has been labeled with an integration (recorder) you are listed as a code owner for? Thanks!

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[bdraco]

Going to get this chain merged, than rebase #87741 and see if it still fails.

If it does I'll start looking into that one.