Closes #45135

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](https://github.com/zed-industries/zed/blob/main/CONTRIBUTING.md#uiux-checklist)

Release Notes:

- Fixed project root name appearing in file paths while searching in
file finder.