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/models/stream_session.rb

@@ -54,11 +54,11 @@ class StreamSession < ApplicationRecord
     end
 
     event :pause do
-      transitions from: %i[live reconnecting], to: :paused
+      transitions from: %i[live reconnecting connecting], to: :paused
     end
 
     event :resume do
-      transitions from: :paused, to: :live
+      transitions from: :paused, to: :connecting
     end
 
     event :finish do
@@ -81,13 +81,30 @@ class StreamSession < ApplicationRecord
     "live/match_#{id}"
   end
 
+  def mediamtx_overlay_path_name
+    "#{mediamtx_path_name}_air"
+  end
+
   def matchlivetv_platform?
     platform == "matchlivetv"
   end
 
   def hls_playback_url
     base = MatchLiveTv.hls_public_url.chomp("/")
-    "#{base}/#{mediamtx_path_name}/index.m3u8"
+    "#{base}/#{effective_hls_path_name}/index.m3u8"
+  end
+
+  def effective_hls_path_name
+    return mediamtx_path_name if terminal?
+    return mediamtx_overlay_path_name unless Streams::OverlayRelay.running?(id)
+    return mediamtx_overlay_path_name if overlay_air_has_output?
+
+    mediamtx_path_name
+  end
+
+  def overlay_air_has_output?
+    info = Mediamtx::Client.new.list_paths.find { |i| i["name"] == mediamtx_overlay_path_name }
+    info && (info["online"] || info["ready"] || info["available"])
   end
 
   def watch_page_url