🐛(backend) preserve recording metadata when updating room access

Updating room access rewrote the entire metadata payload, removing information
about active recordings. This caused the frontend to lose track of ongoing
recordings and could trigger 409 errors when attempting to start a new
recording.

Consolidate the duplicated metadata update logic into
`RoomManagement.update_metadata()` and preserve merge behavior instead of
overwriting the full metadata object.

src/backend/core/services/room_management.py

@@ -8,6 +8,7 @@ from typing import Dict, Optional
 
 from asgiref.sync import async_to_sync
 from livekit.api import (
+    ListRoomsRequest,
     TwirpError,
     UpdateRoomMetadataRequest,
 )
@@ -29,20 +30,45 @@ class RoomManagement:
     """Service for managing LiveKit rooms."""
 
     @async_to_sync
-    async def update_metadata(self, room_name: str, metadata: Optional[Dict] = None):
-        """Update a LiveKit room's metadata.
+    async def update_metadata(
+        self,
+        room_name: str,
+        metadata: Optional[Dict] = None,
+        remove_keys: Optional[list[str]] = None,
+    ):
+        """Merge values into a LiveKit room's metadata.
 
         The `room_name` corresponds to the LiveKit room identifier
         (i.e. the Room model's UUID as a string).
+
+        Raises:
+            RoomNotFoundException: the room does not exist in LiveKit.
+            RoomManagementException: the metadata update otherwise fails.
         """
 
         lkapi = utils.create_livekit_client()
 
         try:
+            response = await lkapi.room.list_rooms(ListRoomsRequest(names=[room_name]))
+
+            if not response.rooms:
+                logger.warning(
+                    "Room %s not found in LiveKit, skipping metadata update",
+                    room_name,
+                )
+                raise RoomNotFoundException("Room does not exist")
+
+            existing_metadata = json.loads(response.rooms[0].metadata or "{}")
+
+            for key in remove_keys or []:
+                existing_metadata.pop(key, None)
+
+            updated_metadata = {**existing_metadata, **(metadata or {})}
+
             await lkapi.room.update_room_metadata(
                 UpdateRoomMetadataRequest(
                     room=room_name,
-                    metadata=json.dumps(metadata) if metadata is not None else "",
+                    metadata=json.dumps(updated_metadata),
                 )
             )