[Feature Request] Copilot App: Full file-tree browser for repository-backed sessions (like folder sessions have)

### Summary

When opening a **folder-backed session**, the app shows a full file-tree browser in the side panel, so I can navigate and open any file in the directory directly. When opening a **repository-backed session** (worktree), the side panel instead shows only a git **Changes** view, which lists *modified* files. With a clean working tree it just says "No files found" / "No changes to compare," and there's no way to browse the repo's files within the app.

### Why this matters

The folder-session file browser is a much nicer integration — it lets me explore and open files without leaving the app or asking the agent. Repository sessions lose that, even though all the files are present on disk in the worktree.

### Request

Add a full file-tree browser to repository-backed sessions (the same explorer that folder sessions already have), ideally alongside the existing git **Changes** view rather than replacing it — e.g. a "Files" tab next to "Changes."

### Repro

1. Open a repository as a session (creates a worktree).
2. With no edits made, look at the side panel.
3. The Changes tab shows "No files found" — there's no way to browse the repo's existing files.

### Expected

Be able to browse and open any file in the repo/worktree from within the app, like folder-backed sessions allow.

Start by comparing the folder-backed session file-tree browser with the repository-backed session's Changes view and trace the side-panel entry point. Add a Files view that can browse and open files in the worktree while preserving Changes, then verify the clean repository repro shows and opens the full tree.

Written by the indexing model from the issue text.