This makes merge conflict resolution clearer because we're now parsing
the branch names from the conflict region instead of hardcoding HEAD and
ORIGIN.

### Before
<img width="1157" height="1308" alt="image"
src="https://github.com/user-attachments/assets/1fd72823-4650-48dd-b26a-77c66d21614d"
/>

### After
<img width="1440" height="1249" alt="Screenshot 2025-12-08 at 2 17
12 PM"
src="https://github.com/user-attachments/assets/d23c219a-6128-4e2d-a8bc-3f128aa55272"
/>

Release Notes:

- git: Use branch names for git conflict buttons instead of HEAD and
ORIGIN