A gateway-backed turn on the runs API executes in the Hermes Gateway, but the
run id only lived in process memory, so a WebUI restart orphaned the turn and
stale-pending repair appended 'Response interrupted' while the run finished
on the gateway.
- persist session.gateway_run {run_id, stream_id} as soon as POST /v1/runs returns
- send Idempotency-Key webui-<stream_id> so the gateway keeps a durable run record
- on startup (after bind, before serving) re-register the stream and follow
GET /v1/runs/{id} until terminal; write back the real output, surface a
parked approval once, keep Stop working, clear the record on every settlement