TASK 31: SceneGraph component + baked-crust compositor optimization

- Add ElementKind (Static/Dynamic) to SceneElement base; Source/WebcamSceneConfig classify
- Services/SceneGraph.cs: owns the Scenes collection (ViewModel's Scenes delegates to it),
  the element mutation surface (Add/Insert/Remove/Move, each invalidating the bake), and the
  queries that were scattered LINQ (GetBackground/GetWebcam/GetChatBoxes/GetSplitPoint/IsStatic)
- SceneCompositor: split-aware BakeStaticBase + CompositeLayers + Render(.., staticBase, split);
  builds/caches the static base below the split point in source-rect space
- FramePump: optional SceneGraph -> optimized bake+composite path; falls back to full render
- MainViewModel: routes element mutations through the graph; invalidates the bake on static
  layout/opacity/visibility/useDefaultBackground changes and after background heal/Ensure
- Integration test SceneGraphTests.BakedStaticBase_WithDynamicLayer_CompositesCorrectly

Derivative survey (mandated): tried before writing — OBS does per-source opacity/visibility
caching and static-scene baking; this mirrors OBS's 'cached static source' optimization.
3 documented defensive deviations from the spec (ChatOverlayLayer stays decoupled;
background helpers stay VM-static for direct testability; full facade peel deferred post-1.0)
in TASKS.md + ai.md. Scope check passed; clean build 0 warnings.

ViewModels/MainViewModel.Scenes.cs

@@ -16,7 +16,10 @@ public partial class MainViewModel
     // TASK 20 step 2 — hotkey bindings (custom chord per action)
     private Dictionary<HotkeyId, HotkeyChord> _hotkeyBindings = new();
 
-    public ObservableCollection<Scene> Scenes { get; } = new();
+    // TASK 31: the scene collection is owned by the SceneGraph (single owner of the
+    // element inventory + mutation surface). The ViewModel exposes it as-is so the
+    // XAML bindings and MainViewModel call sites keep working unchanged.
+    public ObservableCollection<Scene> Scenes => _sceneGraph.Scenes;
 
     public Scene? StagedScene
     {
@@ -36,6 +39,7 @@ public partial class MainViewModel
                     var background = EnsureBackground(value);
                     if (background != null)
                         StampDefaultBackgroundAsset(background, value.Name);
+                    _sceneGraph.InvalidateBake(value);
                 }
                 OnPropertyChanged(nameof(ShowChatInactiveMessage));
                 OnPropertyChanged(nameof(ShowEmptySceneHint));
@@ -251,6 +255,22 @@ public partial class MainViewModel
     {
         if (sender is WebcamSceneConfig && e.PropertyName == nameof(SceneElement.IsVisible))
             OnPropertyChanged(nameof(CanShowWebcamInStagedScene));
+
+        // A Static element's baked pixels depend on its layout, opacity and
+        // visibility — any of those changing invalidates the cached base.
+        if (sender is SceneElement { Kind: ElementKind.Static } el)
+        {
+            var bakedSurface = e.PropertyName is nameof(SceneElement.X) or nameof(SceneElement.Y)
+                or nameof(SceneElement.Width) or nameof(SceneElement.Height)
+                or nameof(SceneElement.Opacity) or nameof(SceneElement.IsVisible)
+                or nameof(SceneElement.ClipShape) or nameof(SceneElement.IsMirrored);
+            if (bakedSurface)
+            {
+                var containingScene = Scenes.FirstOrDefault(s => s.Elements.Contains(el));
+                if (containingScene != null)
+                    _sceneGraph.InvalidateBake(containingScene);
+            }
+        }
         ScheduleSave();
     }