✨(backend) add synchronization mechanism for room configuration updates

Introduce synchronization of room configuration changes across
active participants.

When a room configuration is updated through a PUT operation, the
backend now performs an additional LiveKit API call to notify room
participants through a room metadata update event.

This ensures admins and owners quickly see up-to-date settings in
their administration panel. It also prepares the frontend for
automatic updates of unprivileged participants room’s data without
refetching it from the API.

An event-driven design was chosen instead of storing the full room
configuration in LiveKit metadata. While embedding the state
directly in metadata would provide immediate synchronization, it
would also require initializing and maintaining configuration
state during room creation or webhook handling, increasing the
risk of operational failures and regressions.

Instead, the backend emits lightweight synchronization events and
active clients update their React Query cache, which remains the
single source of truth for room configuration data.

src/backend/core/api/viewsets.py

@@ -77,6 +77,11 @@ from core.services.participants_management import (
     ParticipantsManagementException,
 )
 from core.services.room_creation import RoomCreation
+from core.services.room_management import (
+    RoomManagement,
+    RoomManagementException,
+    RoomNotFoundException,
+)
 from core.services.subtitle import SubtitleException, SubtitleService
 from core.tasks.file import process_file_deletion
 
@@ -300,6 +305,33 @@ class RoomViewSet(
         if callback_id := self.request.data.get("callback_id"):
             RoomCreation().persist_callback_state(callback_id, room)
 
+    def perform_update(self, serializer):
+        """Persist the room update, then sync metadata to LiveKit."""
+
+        old_configuration = serializer.instance.configuration
+        room = serializer.save()
+
+        if room.configuration == old_configuration:
+            return
+
+        metadata = {"configuration": room.configuration}
+
+        try:
+            RoomManagement().update_metadata(
+                room_name=str(room.id),
+                metadata=metadata,
+            )
+        except RoomNotFoundException:
+            logger.info(
+                "LiveKit room %s does not exist yet, skipping metadata sync",
+                room.id,
+            )
+        except RoomManagementException:
+            logger.warning(
+                "Failed to sync metadata to LiveKit for room %s",
+                room.id,
+            )
+
     @decorators.action(
         detail=True,
         methods=["post"],