feat(webcam): resource lifecycle startup slice — poll-on-start, single-cam lock, persistent Layers alert

The creator couldn't add a webcam to Live (grayed app-wide) and nothing in the
app explained why. Ground truth from the live DB: one Webcam identity AND one
WebcamSceneConfig in the Chat scene — so the gray was the single-identity rule
working, but the reason was unobservable. This slice makes the webcam a
resource the app validates and locks, mirroring how OBS reserves its devices.

At startup we enumerate the OS once (ValidateWebcamResourceStartupAsync, fired
after LoadLayout, stored as WebcamStartupValidationTask for tests to await):
- 0 webcams -> app runs on, layer inactive, no alarm
- exactly 1 -> attempt CameraManager.AcquireAsync as an app-wide lock; on
  failure show a persistent red alert at the bottom of the Layers panel
  (WebcamLockAlert + Retry) that re-polls every 5s and clears itself the
  moment the camera locks, or on any first real frame
- >=2 -> deliberately no auto-lock; camera selection belongs to the App
  Settings dialog (gear) — next slice

CameraManager.IsRunning(deviceId) tells the pass a session already exists
(started OR still starting) so loaded identity configs count as the lock and
the pass never double-acquires. Test seams mirror LayoutPathOverride:
CameraEnumeratorOverride / CameraFrameSourceFactoryOverride so the startup
probe never touches real hardware under test.

Good Dog test: WebcamStartupResourceTests x3 — single-cam locked + app runs on,
zero-cams no-alarm/no-lock, lock-fails -> red alert -> Retry -> clears. Full
suite 304/304, build 0 warnings, scope-check passed.

Docs in-commit: TASKS Open items + ai.md Webcam section + HANDOFF rewrite.
Also corrects the record: 'NVIDIA Broadcast opens the webcam exclusively' was a
suspect-list claim (CameraConflictProbe reads process names only, no handles)
— not restated as fact.

Services/CameraManager.cs

@@ -171,6 +171,18 @@ public sealed class CameraManager : IDisposable
         toStop.PreviewBitmap = null;
     }
 
+    /// <summary>
+    /// True while a session exists for the device — started, or still starting.
+    /// Used by the app's startup resource check to avoid double-acquiring a lock
+    /// that the saved identity's scene configs already hold. A rolled-back (failed)
+    /// session is removed, so this goes false and the startup pass can retry.
+    /// </summary>
+    public bool IsRunning(string deviceId)
+    {
+        lock (_gate)
+            return _sessions.ContainsKey(deviceId);
+    }
+
     public VideoFrame? GetLatestFrame(string deviceId)
     {
         lock (_gate)