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TASK 26 superseded by creator directive (app-level resource model).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

@@ -49,6 +49,7 @@ public partial class MainViewModel
                 OnPropertyChanged(nameof(CanAddWebcam));
                 OnPropertyChanged(nameof(CanAddYouTubeChat));
                 OnPropertyChanged(nameof(CanShowWebcamInStagedScene));
+                OnPropertyChanged(nameof(WebcamAddToolTip));
                 OnPropertyChanged(nameof(IsCountdownAvailable));
                 UpdateActiveBackground();
                 UpdateBackgroundImage();