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/public/regia_controller.rb

@@ -1,6 +1,7 @@
 module Public
   class RegiaController < SiteBaseController
     include Public::LiveHelper
+    include MediamtxPlayback
 
     layout "regia"
 
@@ -17,7 +18,7 @@ module Public
       )
       @rules = Scoring::Rules.from_match(@match)
       @stream_closed = @session.terminal?
-      @on_air = !@stream_closed && mediamtx_online?(@session)
+      @on_air = !@stream_closed && mediamtx_stream_playable?(@session)
       @share_url = request.original_url
       @share_title = "Regia — #{@team.name} vs #{@match.opponent_name}"
     end
@@ -61,12 +62,14 @@ module Public
     def status_payload
       score = @session.score_state
       closed = @session.terminal?
+      playable = !closed && mediamtx_stream_playable?(@session)
       {
         status: @session.status,
         paused: @session.paused?,
         stream_closed: closed,
-        live: !closed && (@session.live? || mediamtx_online?(@session)),
-        on_air: !closed && mediamtx_online?(@session),
+        live: !closed && (@session.live? || @session.paused? || mediamtx_publisher_online?(@session)),
+        on_air: playable,
+        publisher_online: !closed && mediamtx_publisher_online?(@session),
         ended_at: @session.ended_at,
         home_name: @session.match.team.name,
         away_name: @session.match.opponent_name,
@@ -74,10 +77,5 @@ module Public
         score: score&.as_cable_payload
       }
     end
-
-    def mediamtx_online?(session)
-      @online_paths_cache ||= Mediamtx::Client.new.online_path_names
-      @online_paths_cache.include?(session.mediamtx_path_name)
-    end
   end
 end