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TASK 26 superseded by creator directive (app-level resource model).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.Webcam.cs

@@ -22,9 +22,30 @@ public partial class MainViewModel
     private string? _webcamLockAlert;
     private DispatcherTimer? _webcamLockPollTimer;
 
-    /// <summary>The Add → Webcam menu item: enabled only while no webcam exists anywhere —
-    /// one camera identity app-wide; re-adding always opens the picker.</summary>
-    public bool CanAddWebcam => StagedScene != null && _webcam == null;
+    /// <summary>
+    /// Add → Webcam menu item: the webcam is an app-level resource (one camera —
+    /// the app default). The row is offered in any scene that doesn't already
+    /// host it, wherever a camera is selected; it is NOT blocked by other scenes
+    /// holding their own placement (per-scene max, not app-wide).
+    /// </summary>
+    public bool CanAddWebcam => StagedScene is { WebcamConfig: null } && _webcam != null;
+
+    /// <summary>
+    /// Why the Webcam row is greyed, when it is — never a silent bool. The max-1
+    /// reason gets the gentle "graduated to OBS" line; no camera at all gets its
+    /// own wording. Shown as the row's tooltip.
+    /// </summary>
+    public string WebcamAddToolTip
+    {
+        get
+        {
+            if (StagedScene?.WebcamConfig != null)
+                return "Already in this scene — one webcam per stream. A second camera means you've graduated to OBS.";
+            if (_webcam == null)
+                return "No webcam detected — plug one in, or allow camera access in Windows.";
+            return "Adds the app default webcam to this scene.";
+        }
+    }
 
     /// <summary>
     /// Right-click-on-preview → "Show Webcam": offered when the active scene has no
@@ -229,6 +250,15 @@ public partial class MainViewModel
         var started = await _cameraManager.AcquireAsync(device.Id);
         if (started)
         {
+            // The single camera becomes the app default so the Web Cam layer is
+            // offered in the capabled scenes (Live/Chat) even on a clean layout.
+            if (_webcam == null)
+            {
+                _webcam = new Webcam { DeviceId = device.Id, Name = device.DisplayName };
+                OnPropertyChanged(nameof(CanChangeWebcam));
+                OnPropertyChanged(nameof(CanAddWebcam));
+                OnPropertyChanged(nameof(WebcamAddToolTip));
+            }
             WebcamLockAlert = null;
             return;
         }
@@ -237,33 +267,28 @@ public partial class MainViewModel
         WebcamLockAlert = $"Web Cam unavailable: {reason}";
     }
 
-    // Adds the webcam to the active scene. The creator ALWAYS picks from the
-    // cameras Windows has registered — never silently resurrects the previous
-    // camera (which is what happened after deleting one scene's webcam while
-    // another scene still used it). Picking a different camera than the current
-    // app-wide one swaps it everywhere, so the single-identity model stays honest;
-    // each scene's placement config is independent (webcam.{scene}.config).
+    // Adds the webcam to the active scene. The webcam is an app-level resource:
+    // once a camera is the app default, adding the layer just places it — the
+    // picker runs only for the initial selection. Each scene's placement config
+    // is independent (webcam.{scene}.config); the camera device is Windows' own
+    // singleton and stays where we put it.
     private async Task AddWebcamToStagedSceneAsync()
     {
         var scene = StagedScene;
         if (scene == null || scene.WebcamConfig != null) return;
 
-        var dialog = new CameraPickerDialog(new CameraPickerViewModel(_cameraEnumerator))
-        {
-            Owner = Application.Current.MainWindow
-        };
-        if (dialog.ShowDialog() != true || dialog.PickedDevice == null) return;
-        var device = dialog.PickedDevice;
-
         if (_webcam == null)
         {
+            var dialog = new CameraPickerDialog(new CameraPickerViewModel(_cameraEnumerator))
+            {
+                Owner = Application.Current.MainWindow
+            };
+            if (dialog.ShowDialog() != true || dialog.PickedDevice == null) return;
+            var device = dialog.PickedDevice;
             _webcam = new Webcam { DeviceId = device.Id, Name = device.DisplayName };
             OnPropertyChanged(nameof(CanChangeWebcam));
             OnPropertyChanged(nameof(CanAddWebcam));
-        }
-        else if (_webcam.DeviceId != device.Id)
-        {
-            await SwapWebcamIdentityAsync(device);
+            OnPropertyChanged(nameof(WebcamAddToolTip));
         }
 
         var config = new WebcamSceneConfig