feat(ui): add current-launch logs tab

Add Live Chat and Logs tabs to the non-edit left panel. Expose a bounded process-local AppLog feed so the newest messages appear first without importing earlier startup.log contents or changing file logging.

Ref: https://obsproject.com/forum/resources/understanding-obs-studio-log.473

ViewModels/MainViewModel.cs

@@ -192,6 +192,7 @@ public partial class MainViewModel : ViewModelBase
     public MainViewModel()
     {
         AppLog.Write("MainViewModel ctor begin");
+        InitializeCurrentLaunchLogs();
         IsAppOwned = _entitlement.IsAppOwned;
         _youtubeAuth = new YouTubeAuthService(OAuthCredentials.ClientId, OAuthCredentials.ClientSecret,
             sessionChanged: ch => TokenStore.Save(ch));
@@ -524,6 +525,7 @@ public partial class MainViewModel : ViewModelBase
 
     public void Shutdown()
     {
+        StopCurrentLaunchLogFeed();
         _saveDebounce?.Stop();
         SaveLayoutNow();
         _fullScreenDetector.StopWatching();