## 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

Closes #52942


## Demo:
### Before:


https://github.com/user-attachments/assets/fd3b69fc-468a-4fd1-82c9-4f1aa83c6474




### After:


https://github.com/user-attachments/assets/0a6c70a9-0a4a-4657-9fe8-21988fff9e80



## Release Notes:

- Fixed play button appearing in gutter for unsaved buffers where
clicking it was a no-op.

---------

Co-authored-by: Lukas Wirth <lukas@zed.dev>