✨(backend) add start-subtitle endpoint

Allow any user, anonymous or authenticated, to start subtitling
in a room only if they are an active participant of it.

Subtitling a room consists of starting the multi-user transcriber agent.
This agent forwards all participants' audio to an STT server and returns
transcription segments for any active voice to the room.

User roles in the backend room system cannot be used
to determine subtitle permissions.

The transcriber agent can be triggered multiple times but will only join a
room once. Unicity is managed by the agent itself.
Any user with a valid LiveKit token can initiate subtitles. Feature flag
logic is implemented on the frontend. The frontend ensures the "start
subtitle" action is only available to users who should see it. The backend
does not enforce feature flags in this version.

Authentication in our system does not imply access to a room. The only
valid proof of access is the LiveKit API token issued by the backend.
Security consideration: A LiveKit API token is valid for 6 hours and
cannot be revoked at the end of a meeting. It is important to verify
that the token was issued for the correct room.

Calls to the agent dispatch endpoint must be server-initiated. The backend
proxies these calls, as clients cannot securely contact the agent dispatch
endpoint directly (per LiveKit documentation).

Room ID is passed as a query parameter. There is currently no validation
ensuring that the room exists prior to agent dispatch.
TODO: implement validation or error handling for non-existent rooms.

The backend does not forward LiveKit tokens to the agent. Default API
rate limiting is applied to prevent abuse.

src/backend/core/tests/services/test_subtitle.py

@@ -0,0 +1,48 @@
+"""
+Test subtitle service.
+"""
+
+# pylint: disable=W0621
+from unittest import mock
+
+import pytest
+
+from core.factories import RoomFactory
+from core.services.subtitle import SubtitleService
+
+pytestmark = pytest.mark.django_db
+
+
+@pytest.fixture
+def mock_livekit_client():
+    """Mock LiveKit API client."""
+    with mock.patch("core.utils.create_livekit_client") as mock_create:
+        mock_client = mock.AsyncMock()
+        mock_create.return_value = mock_client
+        yield mock_client
+
+
+def test_start_subtitle_settings(mock_livekit_client, settings):
+    """Test that start_subtitle uses the configured agent name from Django settings."""
+
+    settings.ROOM_SUBTITLE_AGENT_NAME = "fake-subtitle-agent-name"
+
+    room = RoomFactory(name="my room")
+    SubtitleService().start_subtitle(room)
+
+    mock_livekit_client.agent_dispatch.create_dispatch.assert_called_once()
+
+    call_args = mock_livekit_client.agent_dispatch.create_dispatch.call_args[0][0]
+    assert call_args.agent_name == "fake-subtitle-agent-name"
+    assert call_args.room == str(room.id)
+
+
+def test_stop_subtitle_not_implemented():
+    """Test that stop_subtitle raises NotImplementedError."""
+
+    room = RoomFactory(name="my room")
+
+    with pytest.raises(
+        NotImplementedError, match="Subtitle agent stopping not yet implemented"
+    ):
+        SubtitleService().stop_subtitle(room)