Fix YouTube relay instabile e timer LIVE a zero in app

ffmpeg: probesize/analyzeduration su _air, restart più rapido e avvio relay
al go_live. App: sincronizza started_at dal server e fallback al passaggio live.

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

mobile/lib/providers/session_provider.dart

@@ -111,6 +111,8 @@ class SessionNotifier extends StateNotifier<SessionState> {
         state = state.copyWith(cameraDevice: device);
         return;
       }
+      final startedAt = s.startedAt ??
+          ((incoming == 'live' || incoming == 'reconnecting') ? DateTime.now() : null);
       state = state.copyWith(
         session: StreamSession(
           id: s.id,
@@ -127,7 +129,7 @@ class SessionNotifier extends StateNotifier<SessionState> {
           privacyStatus: s.privacyStatus,
           qualityPreset: s.qualityPreset,
           targetBitrate: s.targetBitrate,
-          startedAt: s.startedAt,
+          startedAt: startedAt,
           disconnectionCount: s.disconnectionCount,
           score: s.score,
           devices: s.devices,