Transitions: fade starts from the outgoing picture (was an instant cut)

The transition started with no from-frame, so BlendFrame returned the new scene at once.
Start now requests a capture and the frame pump supplies its last output on the next tick.
Test: TransitionFadeTests. Docs: ai.md, TASKS.md.

Not pushed.

Services/Encoder/FramePump.cs

@@ -32,6 +32,7 @@ public sealed class FramePump : IDisposable
     private readonly Func<VideoFrame?>? _alertTicker;
     private readonly Func<VideoFrame?>? _brandFlash;
     private readonly TransitionService? _transition;
+    private VideoFrame? _lastOutput;
     private readonly SceneGraph? _sceneGraph;
     private readonly SceneCompositor _compositor = new();
 
@@ -497,6 +498,9 @@ public sealed class FramePump : IDisposable
                     socialBarTicks += sw.ElapsedTicks;
 
                     VideoFrame frame;
+                    if (_transition is { CaptureRequested: true } capture && _lastOutput != null)
+                        capture.SupplyFromFrame(new VideoFrame(_lastOutput.Width, _lastOutput.Height,
+                            (byte[])_lastOutput.BgraPixels.Clone()));
                     var scratchSize = compositorOptions.SourceRectWidth
                         * compositorOptions.SourceRectHeight * 4;
                     renderSw.Restart();
@@ -567,6 +571,7 @@ public sealed class FramePump : IDisposable
                     // tick's buffers are recyclable once the enqueue snapshot them.
                     // The free-list Contains guard keeps the Cut path (BlendFrame
                     // returns toFrame itself, aliasing scratch) safe.
+                    _lastOutput = frame;
                     ReleaseScratch(frame.BgraPixels);
                     ReleaseScratch(scratch);