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/concerns/mediamtx_playback.rb

@@ -0,0 +1,34 @@
+module MediamtxPlayback
+  extend ActiveSupport::Concern
+
+  private
+
+  def mediamtx_paths_index
+    @mediamtx_paths_index ||= Mediamtx::Client.new.list_paths.index_by { |i| i["name"] }
+  end
+
+  def mediamtx_path_info(session, path_name: mediamtx_playback_path_name(session))
+    mediamtx_paths_index[path_name]
+  end
+
+  def mediamtx_playback_path_name(session)
+    session.effective_hls_path_name
+  end
+
+  # Player HLS: path _air con overlay quando il relay è attivo.
+  def mediamtx_stream_playable?(session)
+    return false if session.terminal?
+
+    mediamtx_path_has_output?(session)
+  end
+
+  def mediamtx_path_has_output?(session)
+    info = mediamtx_path_info(session)
+    info && (info["ready"] || info["available"] || info["online"])
+  end
+
+  def mediamtx_publisher_online?(session)
+    info = mediamtx_paths_index[session.mediamtx_path_name]
+    info && info["online"]
+  end
+end