✨(backend) add connection-test API

Currently users have no way to reliably test their connection before
joining a room. We then want to create a connection test page
to adress this issue.

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

We introduce a new API endpoint GET /api/v1.0/connection-test/
to issue a dedicated token for diagnostics, even for anonymous users.
Each request creates a new 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.

src/backend/core/tasks/connection_test.py

@@ -0,0 +1,39 @@
+"""Tasks related to connection test rooms."""
+
+import logging
+
+from django.conf import settings
+
+from core.services.room_management import (
+    RoomManagement,
+    RoomManagementException,
+    RoomNotFoundException,
+)
+from core.tasks._task import task
+
+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
+
+    try:
+        RoomManagement().delete_room(room_name)
+    except RoomNotFoundException:
+        # Room may already be gone after empty/departure timeout.
+        logger.info("Connection test room '%s' already gone.", room_name)
+    except RoomManagementException:
+        logger.exception("Failed to delete connection test room '%s'.", room_name)