🩹(backend) invert operation order in participant handling

Invert operation sequence to first notify people in room before setting
participant in cache. Fixes infinite loop issue caused by 3s cache timeout
for waiting participants when requests take too long. Problem only occurred
when notifications were delayed, as faster notification delivery masked the
race condition.

src/backend/core/services/lobby.py

@@ -221,6 +221,12 @@ class LobbyService:
             color=color,
         )
 
+        try:
+            self.notify_participants(room_id=room_id)
+        except LobbyNotificationError:
+            # If room not created yet, there is no participants to notify
+            pass
+
         cache_key = self._get_cache_key(room_id, participant_id)
         cache.set(
             cache_key,
@@ -228,12 +234,6 @@ class LobbyService:
             timeout=settings.LOBBY_WAITING_TIMEOUT,
         )
 
-        try:
-            self.notify_participants(room_id=room_id)
-        except LobbyNotificationError:
-            # If room not created yet, there is no participants to notify
-            pass
-
         return participant
 
     def _get_participant(