refactor(watch-together): share host peer IDs

lib/watch_together/primitives.dart

@@ -1,5 +1,7 @@
 int watchTogetherSystemNowMs() => DateTime.now().millisecondsSinceEpoch;
 
+String watchTogetherHostPeerId(String sessionId) => 'wt-${sessionId.toUpperCase()}';
+
 bool orderedStringListsEqual(List<String> first, List<String> second) {
   if (first.length != second.length) return false;
   for (var i = 0; i < first.length; i++) {

lib/watch_together/providers/watch_together_provider.dart

@@ -10,6 +10,7 @@ import '../../utils/app_logger.dart';
 import '../models/playback_state.dart';
 import '../models/sync_message.dart';
 import '../models/watch_session.dart';
+import '../primitives.dart';
 import '../services/current_playback_dispatcher.dart';
 import '../services/watch_together_controller.dart';
 import '../services/watch_together_peer_service.dart';
@@ -368,7 +369,7 @@ class WatchTogetherProvider with ChangeNotifier {
       await _peerService!.joinSession(sessionId);
 
       // Session will be fully configured when we receive sessionConfig from host
-      _session = _session!.copyWith(state: SessionState.connected, hostPeerId: 'wt-${sessionId.toUpperCase()}');
+      _session = _session!.copyWith(state: SessionState.connected, hostPeerId: watchTogetherHostPeerId(sessionId));
 
       _displayName = displayName ?? _generateDisplayName();
 

lib/watch_together/services/watch_together_peer_service.dart

@@ -10,6 +10,7 @@ import '../../i18n/strings.g.dart';
 import '../../services/base_peer_service.dart';
 import '../../utils/app_logger.dart';
 import '../models/sync_message.dart';
+import '../primitives.dart';
 
 // Re-export so existing callers that import from here keep working.
 export '../../services/base_peer_service.dart' show PeerError, PeerErrorType;
@@ -352,7 +353,7 @@ class WatchTogetherPeerService with KeepaliveMixin {
 
     _isHost = true;
     _sessionId = sessionId?.toUpperCase() ?? _generateSessionId();
-    _myPeerId = 'wt-$_sessionId';
+    _myPeerId = watchTogetherHostPeerId(_sessionId!);
     _reconnectAttempts = 0;
 
     try {

test/watch_together/primitives_test.dart

@@ -2,6 +2,19 @@ import 'package:flutter_test/flutter_test.dart';
 import 'package:plezy/watch_together/primitives.dart';
 
 void main() {
+  test('host and guest derive the same host peer ID', () {
+    final hostPeerId = watchTogetherHostPeerId('ROOM1');
+    final guestExpectedHostPeerId = watchTogetherHostPeerId('room1');
+
+    expect(guestExpectedHostPeerId, hostPeerId);
+  });
+
+  test('stored room codes preserve the established host peer wire format', () {
+    const persistedSessionId = 'Ab12z';
+
+    expect(watchTogetherHostPeerId(persistedSessionId), 'wt-AB12Z');
+  });
+
   test('orderedStringListsEqual preserves order and multiplicity', () {
     expect(orderedStringListsEqual(const ['a', 'b'], const ['a', 'b']), isTrue);
     expect(orderedStringListsEqual(const ['a'], const ['a', 'b']), isFalse);