feat: Allow task processor to have its own database

[emyller]

Fixes #5136.

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Changes

Based on the original issue (#5136) description.

• Introduce a new router.
• Introduce database settings.
• Handle migrations.

How did you test this code?

• Unit tests.
• Manual testing (new deployments).
• Manual testing (existing deployments).

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[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 71.66667% with 17 lines in your changes missing coverage. Please review.

Project coverage is 97.59%. Comparing base (4aa9e1b) to head (516bbec).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
api/app/routers.py	45.16%	17 Missing ⚠️

❌ Your patch check has failed because the patch coverage (71.66%) is below the target coverage (100.00%). You can increase the patch coverage or adjust the target coverage.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #5406      +/-   ##
==========================================
- Coverage   97.63%   97.59%   -0.04%     
==========================================
  Files        1234     1234              
  Lines       42992    43052      +60     
==========================================
+ Hits        41974    42017      +43     
- Misses       1018     1035      +17     

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[matthewelwell]

Looks good to me, but there are a couple of general comments:

1. I'd love to see in the description confirmation that this has been tested manually
2. We should add these new settings to the docs

[emyller]

@Flagsmith/flagsmith-back-end It makes sense for this router to live here, because the behavior is demanded by the API specifically. However, because it looks very standard for now, it feels like it could be offered by flagsmith-common. What's the team opinion on this? I'm happy to go either path, though I believe testing and docs would be easier if contained in flagsmith[-core].

[emyller]

Yup, moved to flagsmith-common (Flagsmith/flagsmith-common@ec6c2e5), as it was actually necessary. I will update this PR next time I'm working on this, likely on Monday, and resolve this thread afterwards.