Implement sidebar serialization (#52795)

This PR implements basic sidebar deserialization. When the
multiworkspace decides to save itself, it causes the sidebar to
serialize as well. The sidebar can trigger this as well via an event.

Self-Review Checklist:

- [x] I've reviewed my own diff for quality, security, and reliability
- [x] Unsafe blocks (if any) have justifying comments
- [x] The content is consistent with the [UI/UX
checklist](https://github.com/zed-industries/zed/blob/main/CONTRIBUTING.md#uiux-checklist)
- [x] Tests cover the new/changed behavior
- [x] Performance impact has been considered and is acceptable

Release Notes:

- N/A
2e44664ab8Mikayla Maki committed on 3/31/2026, 4:16:35 AM· committed by GitHubparentf3e672c
8 files changedLine totals unavailable