✨(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/tasks/__init__.py

@@ -0,0 +1,9 @@
+"""Celery tasks for the core app."""
+
+from core.tasks.connection_test import delete_connection_test_room
+from core.tasks.file import process_file_deletion
+
+__all__ = (
+    "delete_connection_test_room",
+    "process_file_deletion",
+)

src/backend/core/tasks/connection_test.py

@@ -0,0 +1,51 @@
+"""Tasks related to connection test rooms."""
+
+import logging
+
+from django.conf import settings
+
+from asgiref.sync import async_to_sync
+from livekit.api import (  # pylint: disable=no-name-in-module
+    DeleteRoomRequest,
+    TwirpError,
+)
+
+from core.tasks._task import task
+from core.utils import create_livekit_client
+
+logger = logging.getLogger(__name__)
+
+
+@task
+def delete_connection_test_room(room_name: str):
+    """Force-delete an ephemeral connection-test room.
+
+    Used as a hard cap so a participant cannot keep an auto-refreshed
+    LiveKit session open indefinitely after requesting a test token.
+    """
+    prefix = settings.CONNECTION_TEST_ROOM_PREFIX
+    if not room_name.startswith(prefix):
+        logger.error(
+            "Refusing to delete room '%s': expected prefix '%s'.",
+            room_name,
+            prefix,
+        )
+        return
+
+    async_to_sync(_delete_room)(room_name)
+
+
+async def _delete_room(room_name: str):
+    lkapi = create_livekit_client()
+    try:
+        await lkapi.room.delete_room(DeleteRoomRequest(room=room_name))
+        logger.info("Deleted connection test room '%s'.", room_name)
+    except TwirpError as exc:
+        # Room may already be gone after empty/departure timeout.
+        logger.info(
+            "Could not delete connection test room '%s': %s",
+            room_name,
+            exc,
+        )
+    finally:
+        await lkapi.aclose()