[Requests and ideas] Use context-derived branch names with configurable prefix for worktree sessions

**Mood:** 😔
**Category:** Requests and ideas

## Summary

When GitHub Copilot creates a new worktree session, it auto-generates branch names
in the format `username/random-words` (e.g. `jonathansant/verbose-couscous`).
These names are not meaningful and don't reflect the work being done.

## Proposed Improvements

### 1. Derive the branch slug from the session prompt/context

Copilot already generates a meaningful session name from the prompt — the branch
name should use that same context.

**Current:** `jonathansant/verbose-couscous`
**Proposed:** `feature/update-player-endpoint`

### 2. Let users configure the branch prefix

The prefix before the slug should be configurable in project settings, so teams
can match their own Git conventions.

| Configured prefix | Resulting branch |
|---|---|
| `feature` (default) | `feature/update-player-endpoint` |
| `fix` | `fix/update-player-endpoint` |
| `jonathansant` | `jonathansant/update-player-endpoint` |

## Example

Given a prompt: _"Add negative unit tests for config validation"_

| | Branch name |
|---|---|
| **Current** | `jonathansant/fantastic-bassoon` |
| **Proposed** | `feature/add-negative-unit-tests-for-config` |

## Why This Matters

- Branch names appear in PRs, CI pipelines, and git history — meaningful names
improve team communication
- Aligns with how Copilot already names sessions (context-aware)
- Configurable prefix lets teams follow their own branching conventions

---
| Field | Value |
| --- | --- |
| App version | 0.2.8 |
| OS | macOS 26.5.0 |
| Theme | GitHub |
| Path | /chat |
| Tenure | Week 2 |