Refresh/keep session in sync with external modifications (e.g. via VS Code)

### Feature summary

_No response_

### What problem are you trying to solve?

After implementing something in the app, it's common to e.g. open VS Code to tweak/review/continue manual work. The Github App session is visible inside VS Code, and can be continued there, but the changes aren't picked up back in the Github App; the latter must be restarted for it to reread the session continuation done outside in VS Code.

### Proposed solution

In an ideal world, the App would simply detect external session and show them; since that's probably complicated (two UIs working on the same copilot session), at least some way to refresh the session , similar to what a restart does would help.

### Workflow impact

_No response_

### Installation context

_No response_

### Additional context

Note slight similarity with #1205, though that issue is more about picking up **new** sessions, whereas here it's about picking up continuations of existing/known sessions.

この issue にはファイル、テスト、エントリーポイントが記載されていません。まず、GitHub App が Copilot セッションをどのように読み取るか、また VS Code で作成された継続がアプリの再起動後にどのように表示されるようになるかを追跡してください。既存のセッションを更新して、アプリを再起動せずに外部の変更を表示できれば完了です。

索引モデルが issue の本文から書いたものです。