Use stored home_dir in Docker struct, not literal $HOME (#53642)

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)
- [ ] Tests cover the new/changed behavior
- [x] Performance impact has been considered and is acceptable

Closes #ISSUE

Release Notes:

- N/A
6143af13a3KyleBarton committed on 4/10/2026, 5:56:48 PM· committed by GitHubparenteb76db4
1 file changedLine totals unavailable