fix(pump): slice 7 — take the loop off the UI thread (the 'wait 10ms after render 22ms' contradiction resolved)

Take 10 (59a02a5b, slice 6) finally produced a self-contradicting stat: render
22.4ms + submit 2.5 against a 16.7ms deadline, yet avg wait 10ms — a rebasing
pacer CANNOT sleep after a blown deadline. The wait was queue time: StartAsync
fires from a UI command handler, and async continuations re-capture the current
SynchronizationContext — the 'WPF-free, hermetic' frame pump had been rendering
ON THE DISPATCHER behind the live preview the entire starvation saga. OBS keeps
obs_graphics_thread/video_thread off-UI for exactly this reason (dedicated
threads; see docs.obsproject.com/backend-design 'Libobs Threads').

- FramePump: _pumpTask = Task.Run(() => PumpAsync(...)) — null context inside,
  every continuation stays on the pool.
- Audited, not ignored, what that exposes: StaticPixelCache.Get now locks (pool
  miss-decodes raced UI callers); ChatOverlayLayer.RenderFrame checks its cache
  off-thread but marshals the rare raster MISS to the dispatcher (DrawingVisual
  + RenderTargetBitmap are UI-thread objects) and re-validates there; pump
  events already marshal in the VM.
- GCLatencyMode.SustainedLowLatency for the pump's life (restored in finally).
- Stats gained 'worst render Xms' — bimodal averages hid per-tick spikes.
- Webcam routes through the paste cache (the IsOpaque bypass re-sampled ~156k
  px every tick even between identical device frames).

ONE integration test: Pump_Produces_OffTheStartingContext — an inline-pumping
SynchronizationContext makes the old construction run the resolver on the
starting thread by capture; the loop must never. 70/70 per-class green, clean
build 0 warnings. Docs same commit (ai.md slice 7, TASKS take-11 gate,
MyMistakes #6, HANDOFF). take 11: ~300/300 + honest wait -> saga closed,
Unit B (two-line top bar spec, fully captured) starts.

Services/Compositor/StaticPixelCache.cs

@@ -16,14 +16,19 @@ public static class StaticPixelCache
     public static VideoFrame? Get(string assetId)
     {
         if (string.IsNullOrWhiteSpace(assetId)) return null;
-        if (Cache.TryGetValue(assetId, out var frame)) return frame;
+        // Locked: the frame pump decodes from its own thread now (take-8 off-UI fix),
+        // so the dictionary genuinely races with UI-path callers (snapshots, heals).
+        lock (Cache)
+        {
+            if (Cache.TryGetValue(assetId, out var frame)) return frame;
 
-        var bytes = LayoutStore.Instance?.GetAssetBytes(assetId);
-        if (bytes == null || bytes.Length == 0) return null;
+            var bytes = LayoutStore.Instance?.GetAssetBytes(assetId);
+            if (bytes == null || bytes.Length == 0) return null;
 
-        var decoded = Decode(bytes);
-        if (decoded != null) Cache[assetId] = decoded;
-        return decoded;
+            var decoded = Decode(bytes);
+            if (decoded != null) Cache[assetId] = decoded;
+            return decoded;
+        }
     }
 
     public static VideoFrame? Decode(byte[] bytes)