Default GitHub context not synced across sessions with different app logins

[MariusStorhaug]

Summary

When multiple sessions are open and each logs in with different accounts/apps, the default context marker is not consistent with the active session context.

Reproduction

1. Open Session 1 and log in with app/account App A (set as default at that time).
2. Open Session 2 and log in with app/account App B (set as default at that time).
3. Return to Session 1 and run:
   • Get-GitHubConfig → shows App B as default context.
   • Get-GitHubContext → returns info about App A.
   • Get-GitHubContext -ListAvailable → default marker is on App B.
   • Get-GitHubApp (current session was logged in using an app) shows session/account behavior inconsistent with default marker.

Actual behavior

Default context marker/state appears to be updated globally across sessions, while session-resolved context still points to the session login.

Expected behavior

Behavior should be predictable in multi-session usage and configurable:

1. Operational default should be session-local by default

   • A session keeps its selected active/default context stable unless changed in that same session.

2. A separate global startup default should exist for new sessions

   • New sessions initialize from a global default context, but existing sessions do not switch automatically.

3. Shared contexts should remain available across sessions

   • Sessions can list/select shared contexts, but accessing them should not implicitly change another session's active default.

4. Configuration option for default scope

   • Add a setting (for example, DefaultContextScope) to choose behavior:
     • Session (recommended)
     • Global
   • Optionally pair with StartupDefaultContext for session initialization.

Commands should consistently reflect the same effective context model:

• Get-GitHubConfig
• Get-GitHubContext
• Get-GitHubContext -ListAvailable
• Get-GitHubApp