[Feature] Enable to `git add` reviewed files changed

I would love to have a "Git" integrated feature, where when reviewing "Files changed", I could stage reviewed files (as if they'd been `git add`-ed).

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| Field | Value |
| --- | --- |
| App version | 1.1.8 |
| OS | macOS 26.5.0 |
| Theme | GitHub |
| Path | /chat |
| Tenure | Week 8 |

Start by tracing the Files changed review flow from /chat and locating the app entry point for Git-related actions. Determine how reviewed files are represented and how staging should be exposed; done means reviewed files can be staged as though git add was run, with the behavior verified in the app.

Written by the indexing model from the issue text.