♻️ refactor : PLAYER_LIST 여러번 브로드캐스팅 방지

Author: silver-eunjoo

backend/src/main/java/io/f1/backend/domain/game/app/RoomService.java

@@ -338,8 +338,6 @@ public void exitRoomForDisconnectedPlayer(Long roomId, Player player, String ses
             SystemNoticeResponse systemNoticeResponse =
                     ofPlayerEvent(player.nickname, RoomEventType.EXIT);
 
-            messageSender.sendBroadcast(
-                    destination, MessageType.PLAYER_LIST, toPlayerListResponse(room));
             messageSender.sendBroadcast(
                     destination, MessageType.SYSTEM_NOTICE, systemNoticeResponse);
         }
@@ -366,5 +364,10 @@ public void handleDisconnectedPlayers(Room room, List<Player> disconnectedPlayer
             String sessionId = room.getSessionIdByUserId(player.getId());
             exitRoomForDisconnectedPlayer(room.getId(), player, sessionId);
         }
+
+        String destination = getDestination(room.getId());
+
+        messageSender.sendBroadcast(
+            destination, MessageType.PLAYER_LIST, toPlayerListResponse(room));
     }
 }