Reduce code duplication in provider handlers

[jhrozek]

Summary

This is a refactor that's split off PR #3348 and merging it will make my life easier while I'm maintaining the whole branch.

Relates: #3263

Change Type

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• Bug fix (resolves an issue without affecting existing features)
• Feature (adds new functionality without breaking changes)
• Breaking change (may impact existing functionalities or require documentation updates)
• Documentation (updates or additions to documentation)
• Refactoring or test improvements (no bug fixes or new functionality)

Testing

Outline how the changes were tested, including steps to reproduce and any relevant configurations.
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Review Checklist:

• Reviewed my own code for quality and clarity.
• Added comments to complex or tricky code sections.
• Updated any affected documentation.
• Included tests that validate the fix or feature.
• Checked that related changes are merged.

[stacklokbot]

✅ No Invisible Unicode Characters Detected.

[coveralls]

coverage: 49.423% (+0.005%) from 49.418%
when pulling 4c8c550 on jhrozek:handler_duplication
into e2336a5 on stacklok:main.