Add git awareness to file tab icons (#16637)

Before:
<img width="536" alt="Screenshot 2024-08-22 at 15 58 22"
src="https://github.com/user-attachments/assets/7d957f82-cb09-451e-b944-28d57220a718">

After:
<img width="542" alt="Screenshot 2024-08-22 at 15 58 32"
src="https://github.com/user-attachments/assets/fc203c90-903a-4c35-8af0-45cca66cb9d6">


Release Notes:

- N/A

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Co-authored-by: evrensen467 <146845123+evrensen467@users.noreply.github.com>