🐛(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/utils.py

@@ -31,7 +31,6 @@ from livekit.api import (  # pylint: disable=E0611
     LiveKitAPI,
     SendDataRequest,
     TwirpError,
-    UpdateRoomMetadataRequest,
     VideoGrants,
 )
 
@@ -258,57 +257,6 @@ async def notify_participants(room_name: str, notification_data: dict):
         await lkapi.aclose()
 
 
-class MetadataUpdateException(Exception):
-    """Room's metadata update fails."""
-
-
-@async_to_sync
-async def update_room_metadata(
-    room_name: str, metadata: dict, remove_keys: Optional[list[str]] = None
-):
-    """Update LiveKit room metadata by merging new values with existing metadata.
-
-    Args:
-        room_name: Name of the room to update
-        metadata: Dictionary of metadata key-values to add/update
-        remove_keys: Optional list of keys to remove from existing metadata.
-    """
-
-    lkapi = create_livekit_client()
-
-    try:
-        response = await lkapi.room.list_rooms(
-            ListRoomsRequest(
-                names=[room_name],
-            )
-        )
-
-        if not response.rooms:
-            return
-
-        room = response.rooms[0]
-
-        existing_metadata = json.loads(room.metadata) if room.metadata else {}
-
-        if remove_keys:
-            for key in remove_keys:
-                existing_metadata.pop(key, None)
-
-        updated_metadata = {**existing_metadata, **metadata}
-
-        await lkapi.room.update_room_metadata(
-            UpdateRoomMetadataRequest(
-                room=room_name, metadata=json.dumps(updated_metadata).encode("utf-8")
-            )
-        )
-    except TwirpError as e:
-        raise MetadataUpdateException(
-            f"Failed to update metadata for room {room_name}: {e}"
-        ) from e
-    finally:
-        await lkapi.aclose()
-
-
 ALPHANUMERIC_CHARSET = string.ascii_letters + string.digits