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.

ViewModels/MainViewModel.Webcam.cs

@@ -1,7 +1,10 @@
+using System.Collections.Generic;
 using System.Windows;
 using System.Windows.Input;
 using System.Windows.Media.Imaging;
+using System.Windows.Threading;
 using ytLive;
+using ytLive.Helpers;
 using ytLive.Models;
 using ytLive.Services;
 
@@ -16,6 +19,8 @@ public partial class MainViewModel
     private readonly CameraManager _cameraManager;
     private Webcam? _webcam;
     private string? _webcamError;
+    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>
@@ -45,6 +50,37 @@ public partial class MainViewModel
         private set => SetProperty(ref _webcamError, value);
     }
 
+    // Startup resource validation keeps its task for tests to await (the real
+    // app fires it fire-and-forget from the ctor).
+    internal Task? WebcamStartupValidationTask { get; private set; }
+
+    /// <summary>
+    /// Red alert shown at the bottom of the Layers panel when the one-and-only
+    /// detected webcam could NOT be locked at startup. Persistent: while set, a
+    /// light re-poll re-runs the lock check so the moment the camera frees up
+    /// (another app closed) the alert clears itself; a Retry button does it now.
+    /// </summary>
+    public string? WebcamLockAlert
+    {
+        get => _webcamLockAlert;
+        private set
+        {
+            if (!SetProperty(ref _webcamLockAlert, value)) return;
+            if (value == null)
+            {
+                _webcamLockPollTimer?.Stop();
+            }
+            else if (_webcamLockPollTimer == null)
+            {
+                _webcamLockPollTimer = new DispatcherTimer { Interval = TimeSpan.FromSeconds(5) };
+                _webcamLockPollTimer.Tick += (_, _) => _ = ValidateWebcamResourceStartupAsync();
+                _webcamLockPollTimer.Start();
+            }
+        }
+    }
+
+    public ICommand RetryWebcamLockCommand { get; }
+
     // Webcam size safeguard: no more than half the frame in any dimension
     // (960x540 over the 1920x1080 master), and no less than 10% of it
     // (192x108). Enforced at resize and on layout load. The Chat scene is
@@ -135,6 +171,7 @@ public partial class MainViewModel
     {
         if (_webcam?.DeviceId != deviceId) return;
         WebcamError = null;
+        WebcamLockAlert = null; // the camera is provably alive — alert resolved.
         foreach (var scene in Scenes)
             foreach (var config in scene.Elements.OfType<WebcamSceneConfig>())
                 config.VideoImageSource = bitmap;
@@ -148,6 +185,58 @@ public partial class MainViewModel
         WebcamError = $"Webcam offline: {message}";
     }
 
+    /// <summary>
+    /// Runs exactly once at startup (and on Retry): enumerate the OS webcams,
+    /// then tri-state:
+    /// 0 → no alarm, layer inactive.
+    /// 1 → try to lock; failure → persistent red alert (re-poll every 5 s).
+    /// ≥2 → leave to the settings-dialog selector (next slice).
+    /// Re-running after a failure re-enumerates then retries the lock; a real
+    /// frame arriving (first-frame proof) also clears the alert.
+    /// </summary>
+    internal async Task ValidateWebcamResourceStartupAsync()
+    {
+        IReadOnlyList<CameraDeviceInfo> cameras;
+        try
+        {
+            cameras = await _cameraEnumerator.GetCamerasAsync();
+        }
+        catch (Exception ex)
+        {
+            AppLog.Write($"WebcamResource: enumeration failed: {ex.Message}");
+            WebcamLockAlert = "Web Cam unavailable — couldn't enumerate cameras.";
+            return;
+        }
+
+        var count = cameras?.Count ?? 0;
+        if (count != 1)
+        {
+            // 0: no camera; ≥2: settings-dialog selector (next slice).
+            WebcamLockAlert = null;
+            return;
+        }
+
+        var device = cameras![0];
+
+        // A session already started/starting for this device (loaded identity)
+        // means we already hold the lock — nothing to do.
+        if (_cameraManager.IsRunning(device.Id))
+        {
+            WebcamLockAlert = null;
+            return;
+        }
+
+        var started = await _cameraManager.AcquireAsync(device.Id);
+        if (started)
+        {
+            WebcamLockAlert = null;
+            return;
+        }
+
+        var reason = WebcamError ?? "the camera could not be locked.";
+        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