Get Connection Check Token

Mint a LiveKit token for a throwaway room, so the browser can run livekit-client's ConnectionCheck suite before joining a real class.

NOT a token for the class they are about to enter. ConnectionCheck opens and closes up to eight separate room connections (websocket, webrtc, turn, protocol, publish audio, publish video...). Pointed at the real room, a student running it thirty seconds before the bell would appear and vanish from the roster eight times, fire eight rounds of participant events at everyone already inside, and be indistinguishable from a student with a flapping connection. So the check gets its own room.

The room name is derived from the user id rather than random, so one person running the check repeatedly reuses a single empty LiveKit room instead of stranding a new one on each attempt. The room is created implicitly by the first connect and reaped by LiveKit once it empties.