Feature: Branch per workdir on user

As discussed before, to make it easier and simpler to work in parallel, we can separate our logic for the workdir we use for running and writing tests into one folder per branch. This will make it possible to work with different branches in the same browser in multiple tabs, or even in the UI tab.

Create separate folders for each branch so multiple test tabs can run simultaneously without conflicts.

Current Problem:
- Single directory shared across branches
- Can't run multiple tabs at once

Solution:
- Each branch checkout = new folder
- Multiple tabs can work independently

Implementation:
1. When user switches branch in UI → create new folder
2. Sparse checkout in the new folder
3. Keep semantic search running from main repo only
4. Each tab works in its own branch folder