Get Agent Dispatch Status

Read-only agent-dispatch state for the client's first-join wait (A1).

While the LiveKit room is up but no agent announced session_ready, the client probes this to decide whether to keep waiting: claim_pending is True exactly while an agent is still destined for the room (queued request, fresh claim still connecting, or a rerequest marker parked on an active lease — the resume race, where the old runtime's lease outlives its pipeline until after the recording upload).

Deliberately minimal (B-P2-5b): this is a PUBLIC participant endpoint, so it exposes exactly the one bit the client's wait decision needs — internal run-status strings stay internal (worker logs/staff surfaces own them).