refactor: extract ChatOverlayLayer — real component decomposition, Commit G

The first true decomposition of the 4105-line god-object, not another partial
shuffle. MainViewModel.Chat.cs 194 -> 44 lines of thin delegation; all chat
behavior now lives in a self-contained Services/ChatOverlayLayer.cs (199):

- Owns the message buffer (Messages), ChatBoxRenderer, fade + mock-preview
  timers, per-source preview renders, and the live-output RenderFrame path.
- The VM keeps only the binding surface: ChatMessages delegates to
  _chatLayer.Messages (so XAML ItemsSource + LeftPanel CollectionChanged hold),
  CanAddYouTubeChat / ShowChatInactiveMessage stay computed on the VM
  (OnPropertyChanged raised from VM setters + XAML-bound), and thin forwards.
- Scenes handed in as args (no Func seam), so the layer owns no scene graph.

An AI reading ChatOverlayLayer.cs now sees the entire chat feature in one
self-contained unit. Zero behavior change; build 0 warnings; 246 pass, only the
2 known failures. Docs: ViewModels/index.md tracker updated in same commit.

ViewModels/MainViewModel.cs

@@ -274,7 +274,7 @@ public partial class MainViewModel : ViewModelBase
         _screenCaptureManager.CaptureFailed += (key, message) =>
             AppLog.Write($"ScreenCaptureManager: capture '{key}' failed: {message}");
 
-        _chatBoxRenderer = new ChatBoxRenderer();
+        _chatLayer = new ChatOverlayLayer(new ChatBoxRenderer());
 
         _rtmpUrlProvider = () => _reusableStreamUrl; // TASK 5: the reusable stream's ingest URL
         _framePump = new FramePump(