✨(backend) add lobby cache clearing method for meeting conclusion

Implement new lobby service method to clear all participant entries from cache.

Lays foundation for upcoming feature where participant permissions reset when
meetings end. Currently introduces only the cache clearing functionality;
event handling for meeting conclusion will be implemented in future commits

src/backend/core/services/lobby_service.py

@@ -356,3 +356,14 @@ class LobbyService:
             raise LobbyNotificationError("Failed to notify room participants") from e
         finally:
             await lkapi.aclose()
+
+    def clear_room_cache(self, room_id: UUID) -> None:
+        """Clear all participant entries from the cache for a specific room."""
+
+        pattern = self._get_cache_key(room_id, "*")
+        keys = cache.keys(pattern)
+
+        if not keys:
+            return
+
+        cache.delete_many(keys)