Before you mark this PR as ready for review, make sure that you have:
- [x] Added a solid test coverage and/or screenshots from doing manual
testing
- [x] Done a self-review taking into account security and performance
aspects
- [x] Aligned any UI changes with the UI checklist

Release Notes:

- Fixed context server availability updates when a new worktree is added
to or removed from a project.

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Co-authored-by: Ben Brandt <benjamin.j.brandt@gmail.com>