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>

backend/app/controllers/api/v1/stream_sessions_controller.rb

@@ -34,6 +34,11 @@ module Api
         render json: session_json(@session)
       end
 
+      def score
+        Scoring::SyncState.new(session: @session, payload: score_sync_params).call
+        render json: session_json(@session, detail: true)
+      end
+
       def events
         events = @session.stream_events.recent.limit(100)
         render json: events.map { |e| event_json(e) }
@@ -126,6 +131,13 @@ module Api
         params.permit(:platform, :privacy_status, :quality_preset, :target_bitrate, :target_fps, :youtube_channel)
       end
 
+      def score_sync_params
+        params.permit(
+          :home_sets, :away_sets, :home_points, :away_points, :current_set,
+          set_partials: %i[set home away]
+        )
+      end
+
       def session_json(session, detail: false)
         data = {
           id: session.id,