Integrate direct WebSocket-based leaderboard functionality for real-time updates and requests. Refactor related client-side logic to utilize this new connection.

cmd/client/main.go

@@ -367,7 +367,10 @@ func (g *Game) updateLobby() {
 
 	// Spiel wurde gestartet?
 	if g.gameState.Status == "COUNTDOWN" || g.gameState.Status == "RUNNING" {
-		g.appState = StateGame
+		if g.appState != StateGame {
+			g.appState = StateGame
+			g.notifyGameStarted() // Benachrichtige JavaScript dass Spiel startet
+		}
 	}
 }