Title: Initial user prompt lost when Git setup/snapshot command times out

Title: Initial user prompt lost when Git setup/snapshot command times out

Body:
A new Copilot app session lost the user’s initial prompt after a Git command timed out after 300 seconds.

Observed behavior:

The UI showed a Git timeout: git command timed out after 300 seconds.
The prompt did not return.
Stuck Git processes remained running, including git worktree add, git reset --hard --no-recurse-submodules, and git add -A.
After recovery, the persisted chat context did not include the original user request.
The earliest stored user message was only the later follow-up: what happened?.
Expected behavior:
The initial prompt should be persisted before or independently of long-running Git setup/snapshot operations, so it can be recovered even if Git times out or child processes remain stuck.

Impact:
Users can lose their original request and cannot recover the intended task without retyping it

---
| Field | Value |
| --- | --- |
| App version | 1.0.21 |
| OS | Windows 10.0.26200 |
| Theme | GitHub |
| Path | /chat |

レポートではソースファイルもテストも指定されていません。まず /chat パスで Git setup/snapshot のタイムアウトフローを再現し、初期プロンプトがいつ永続化されるかを追跡してください。タイムアウトした、またはスタックした Git 操作が発生しても元のプロンプトを復元でき、その復元をカバーする回帰テストがあることを完了条件とします。

索引モデルが issue の本文から書いたものです。