feat(ui): show YouTube-confirmed live state in top bar

Normal ON-AIR stays red until YouTube reports lifeCycleStatus=live, then turns green; TEST stays gold and stop restores the idle color.

Status-color reference: https://www.carbondesignsystem.com/building-blocks/core/patterns/status-indicators

ViewModels/MainViewModel.Streaming.cs

@@ -24,6 +24,7 @@ public partial class MainViewModel : ViewModelBase
     /// <summary>Latches once the broadcast reaches live so the per-poll broadcast
     /// diagnostic stops logging (2026-10-04). Reset at broadcast creation.</summary>
     private bool _broadcastSeenLive;
+    private bool _youtubeBroadcastLive;
     private string? _reusableStreamUrl;
     private ReusableStream? _reusableStream;
     private string? _healthIssueBanner;
@@ -63,6 +64,7 @@ public partial class MainViewModel : ViewModelBase
         {
             if (SetProperty(ref _streamStatus, value))
             {
+                _youtubeBroadcastLive = false;
                 OnPropertyChanged(nameof(IsOffline));
                 OnPropertyChanged(nameof(IsLive));
                 OnPropertyChanged(nameof(IsEditMode));
@@ -373,6 +375,22 @@ public partial class MainViewModel : ViewModelBase
         set => SetProperty(ref _topBarBackground, value);
     }
 
+    internal void ApplyBroadcastLifecycleStatus(string? lifeCycleStatus)
+    {
+        if (!IsLive) return;
+        if (!string.Equals(lifeCycleStatus, "live", StringComparison.OrdinalIgnoreCase))
+        {
+            if (!_broadcastSeenLive)
+                _healthPollTimer.Interval = TimeSpan.FromSeconds(2);
+            return;
+        }
+
+        _broadcastSeenLive = true;
+        _youtubeBroadcastLive = true;
+        _healthPollTimer.Interval = TimeSpan.FromSeconds(30);
+        UpdateLiveVisuals();
+    }
+
     public string PreviewGlowBrush
     {
         get => _previewGlowBrush;