feat(webcam): app-default gate slice — per-scene offer, Add places default directly, identity survives removal

Chat's camera no longer greys Web Cam in Live (per-scene max, not app-wide);
TASK 26 superseded by creator directive (app-level resource model). Add Webcam
now places the existing app default without the picker; the picker runs only
for the initial selection. Removing the last placement keeps the identity
(_webcam never nulled) so Add stays offered. Startup pass adopts a solo camera
as the app default, so a clean layout offers the layer in Live/Chat at once.
Dynamic WebcamAddToolTip names the why (incl. the 'graduated to OBS' line).

Good Dog: WebcamMenuGateTests rewritten (real app + temp DB + camera seams) —
identity in Chat does not gray Live; Add in Live places same wc-1 no picker;
scene-with-placement stays gray; identity survives both removals (DB row 1).
WebcamStartupResourceTests single-lock fact asserts CanAddWebcam after adoption.
Docs same commit (ai.md supersession, TASKS.md, HANDOFF.md). 304/304, 0 warnings.

ViewModels/MainViewModel.Sources.cs

@@ -217,9 +217,9 @@ public partial class MainViewModel
 
     // Removes an element from the active scene. For a webcam config this drops the
     // scene's usage and releases one camera reference (CameraManager stops the
-    // session when the last using scene lets go). When the last config anywhere is
-    // removed, the webcam identity is cleared too — re-adding opens the picker
-    // again instead of silently resurrecting the old camera.
+    // session when the last using scene lets go). The webcam identity survives —
+    // it's the app-level default, so removing a scene's placement re-enables Add
+    // for the same camera instead of dropping it.
     private void RemoveElement(SceneElement? element)
     {
         var scene = StagedScene;
@@ -235,13 +235,11 @@ public partial class MainViewModel
             _webView2Manager?.Unregister(webSource.Id);
         _sceneGraph.RemoveElement(scene, element);
 
-        if (element is WebcamSceneConfig && _webcam != null
-            && !Scenes.Any(s => s.Elements.OfType<WebcamSceneConfig>().Any()))
+        if (element is WebcamSceneConfig)
         {
-            _webcam = null;
-            OnPropertyChanged(nameof(CanChangeWebcam));
             OnPropertyChanged(nameof(CanAddWebcam));
             OnPropertyChanged(nameof(CanShowWebcamInStagedScene));
+            OnPropertyChanged(nameof(WebcamAddToolTip));
         }
 
         OnPropertyChanged(nameof(ShowEmptySceneHint));