Enable file picker and markdown editor before submitting first prompt of session

### Feature summary

When opening a new session, user can see file picker in right rail and direclty edit, save, and commit files before first session in the prompt

### What problem are you trying to solve?

### TL;DR
As a user curating agent context in my repo, I often want to direclty edit files _before_ I engage an agent. For example, I may want to write a spec or product hypothesis, and then work with an agent to spar on that idea.

### Proposed solution

### Current state:
- Start session
- Right rail not availabel
- Sumbit first prompt of session
- Right rail option appears
- Click right rail, choose file picker, edit files

### Ideal state:
- Start session (local, worktree, etc.)
- RIght rail with file picker appears
- Choose file, edit, and then submit first prompt
- All changes should be able to be saved and commited before first prompt

### Workflow impact

### Why it's worth investing in

- Keeps user in GH app. The absence of a pre-session file picker and editor experience drives users to secondary editors (VS Code, Obsidian, etc.) outside of GH app. Introduces opportuntiy for incomplete session + creates context switching overhead for user.

### Installation context

_No response_

### Additional context

_No response_

Start from the session-start flow and the right-rail visibility condition described in the issue; trace how the file picker, markdown editor, save, and commit actions become available after the first prompt. Done means a new local or worktree session exposes the right rail before the first prompt and lets users choose, edit, save, and commit files.

Written by the indexing model from the issue text.