✨(backend) add connection-test API

Currently users have no way to reliably test their connection before
joining a room. To address this, we plan to build a connection-test
page.

The testing requires a dedicated LiveKit token, issued without going
through the room API, which is tied to registered meetings, lobby
rules, and longer-lived access tokens.

Introduce a new viewset for all diagnostics-related features. The
first route issues a token for diagnostics, even for anonymous
users. Each request creates a new dedicated room so users never
share the same LiveKit room during tests. Tokens are short-lived
(default 10 minutes) to limit reuse, and the endpoint is throttled
to prevent abuse.

A Celery worker also schedules a callback that deletes the room
after a certain delay, in every case.

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 (
+    DeleteRoomRequest,
     ListRoomsRequest,
     TwirpError,
     UpdateRoomMetadataRequest,
@@ -88,3 +89,30 @@ class RoomManagement:
 
         finally:
             await lkapi.aclose()
+
+    @async_to_sync
+    async def delete_room(self, room_name: str):
+        """Delete a LiveKit room and disconnect all participants.
+
+        Raises:
+            RoomNotFoundException: the room does not exist in LiveKit.
+            RoomManagementException: the deletion otherwise fails.
+        """
+
+        lkapi = utils.create_livekit_client()
+
+        try:
+            await lkapi.room.delete_room(DeleteRoomRequest(room=room_name))
+            logger.info("Deleted LiveKit room %s", room_name)
+        except TwirpError as e:
+            if e.code == "not_found":
+                logger.warning(
+                    "Room %s not found in LiveKit, skipping deletion",
+                    room_name,
+                )
+                raise RoomNotFoundException("Room does not exist") from e
+
+            logger.exception("Unexpected error deleting room %s", room_name)
+            raise RoomManagementException("Could not delete room") from e
+        finally:
+            await lkapi.aclose()