Readiness probe. Wire this to readinessProbe and to load balancers.

Sync endpoints run in the anyio threadpool, so a saturated pool means the server cannot serve real traffic even though the event loop still turns. This handler stays async on purpose: a sync handler would borrow a token of the pool it is measuring, adding load exactly when there is none to spare, and would queue rather than answer. Liveness lives at /health.