Aggiunge overlay server-side burn-in e stabilizza diretta live.

Tabellone, badge e brand sono ricodificati nel flusso _air via OverlayRelay;
sync punteggio HTTP, volume condiviso rails/sidekiq, qualità 720p migliorata
e badge CONNECTING in ripresa da pausa.

Co-authored-by: Cursor <cursoragent@cursor.com>

mobile/lib/shared/widgets/live_score_controls.dart

@@ -1,10 +1,12 @@
+import 'dart:async';
+
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
 
 import '../../app/theme.dart';
 import '../../features/shared/live_score_actions.dart';
 import '../../providers/score_provider.dart';
-import '../websocket_service.dart';
+import '../../providers/score_sync_provider.dart';
 import 'score_overlay_bar.dart';
 
 /// Tabellone interattivo: aggiorna punteggio via WebSocket (senza link regia).
@@ -27,8 +29,8 @@ class LiveScoreControls extends ConsumerWidget {
   final Future<void> Function()? onStopStream;
 
   void _sync(WidgetRef ref) {
-    if (!ref.read(websocketServiceProvider).isConnected) return;
-    ref.read(websocketServiceProvider).sendScoreUpdate(ref.read(scoreProvider));
+    // HTTP serializzato; il server fa broadcast WebSocket. Pagina live = status.json.
+    unawaited(ref.read(scoreSyncProvider).push());
   }
 
   Future<void> _pointHome(BuildContext context, WidgetRef ref) async {