♻️(all) stop relying on cookies for the lobby flow

The lobby system relied on cookies to identify the participant
across the wait/enter cycle, which does not work in an iframe
context where our cookies are dropped.

Simplify the lobby behavior:

* The POST request that enters the lobby now returns the
  participant id in the response.
* The frontend passes that id back on subsequent requests to keep a
  sticky session while trying to enter the room.

This moves a bit more logic to the frontend but should be a
transparent refactoring, without decreasing the security of the
lobby flow.

src/backend/core/api/viewsets.py

@@ -616,13 +616,10 @@ class RoomViewSet(
 
         participant, livekit = lobby_service.request_entry(
             room=room,
-            request=request,
+            user=request.user,
             **serializer.validated_data,
         )
-        response = drf_response.Response({**participant.to_dict(), "livekit": livekit})
-        lobby_service.prepare_response(response, participant.id)
-
-        return response
+        return drf_response.Response({**participant.to_dict(), "livekit": livekit})
 
     @decorators.action(
         detail=True,