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.

El issue no menciona archivos, pruebas ni puntos de entrada. Empieza rastreando cómo la GitHub App lee las sesiones de Copilot y cómo las continuaciones realizadas en VS Code pasan a ser visibles después de reiniciar la app; el trabajo estará terminado cuando una sesión existente pueda actualizarse para mostrar cambios externos sin reiniciar la app.

Escrito por el modelo de indexación a partir del texto del issue.