fix: suppress position sync when app backgrounded

lib/screens/video_player_screen.dart

@@ -472,6 +472,10 @@ class VideoPlayerScreenState extends State<VideoPlayerScreen> with WidgetsBindin
       return;
     }
 
+    // Suppress Watch Together heartbeats while backgrounded so App Nap
+    // doesn't cause stale position broadcasts that make guests loop.
+    _watchTogetherProvider?.setBackgrounded(true);
+
     final currentPlayer = player;
     if (currentPlayer == null || !_isPlayerInitialized) {
       _recordLifecycleState('hidden', action: 'skipped_no_player');
@@ -511,6 +515,7 @@ class VideoPlayerScreenState extends State<VideoPlayerScreen> with WidgetsBindin
 
   Future<void> _handleAppResumed() async {
     _recordLifecycleState('resumed', action: 'begin');
+    _watchTogetherProvider?.setBackgrounded(false);
 
     if (Platform.isAndroid && _androidAutoPipTransitionInFlight && !PipService().isPipActive.value) {
       _setAndroidAutoPipTransitionInFlight(false, reason: 'resume_without_pip');

lib/watch_together/providers/watch_together_provider.dart

@@ -402,6 +402,11 @@ class WatchTogetherProvider with ChangeNotifier {
     appLogger.d('WatchTogether: Player detached from sync manager');
   }
 
+  /// Suppress position sync while the app is backgrounded.
+  void setBackgrounded(bool value) {
+    _syncManager?.setBackgrounded(value);
+  }
+
   /// Set up listeners for peer service events
   void _setupPeerServiceListeners() {
     _peerConnectedSubscription = _peerService!.onPeerConnected.listen((peerId) {

lib/watch_together/services/watch_together_sync_manager.dart

@@ -79,6 +79,9 @@ class WatchTogetherSyncManager {
   // Whether we've announced our player as ready (first buffering: false)
   bool _hasAnnouncedReady = false;
 
+  // Whether the app is backgrounded (suppress heartbeats to avoid stale positions)
+  bool _backgrounded = false;
+
   // Callbacks
   SessionConfigCallback? onSessionConfigReceived;
   SyncStateCallback? onSyncStateChanged;
@@ -204,6 +207,7 @@ class WatchTogetherSyncManager {
     }
     _positionSyncTimer?.cancel();
     _positionSyncTimer = null;
+    _backgrounded = false;
 
     appLogger.d('WatchTogether: Player detached');
   }
@@ -313,7 +317,7 @@ class WatchTogetherSyncManager {
   void _startPositionSync() {
     _positionSyncTimer?.cancel();
     _positionSyncTimer = Timer.periodic(positionSyncInterval, (_) {
-      if (_player != null && _session.isHost) {
+      if (_player != null && _session.isHost && !_backgrounded) {
         _peerService.broadcast(
           SyncMessage.positionSync(
             _player!.state.position,
@@ -956,6 +960,16 @@ class WatchTogetherSyncManager {
     }
   }
 
+  /// Suppress heartbeats while the app is backgrounded.
+  ///
+  /// macOS App Nap can throttle the event loop, causing stale position reads.
+  /// Guests would drift-correct to the stale position every heartbeat, making
+  /// playback loop. Pausing heartbeats avoids this; drift correction catches
+  /// up when the app returns to the foreground.
+  void setBackgrounded(bool value) {
+    _backgrounded = value;
+  }
+
   /// Re-announce player readiness after reconnect.
   ///
   /// During reconnect the host resets our _peerReady entry to false via