Api Run

Deep readiness check that exercises the SQLAlchemy pool (ORO-1121). Acquires a session and runs SELECT 1 with a hard timeout, retrying once on failure to ride out transient pool stalls or one-shot network blips (ORO-1168). If the pool is wedged (phantom-checked-out slots) or RDS is unreachable across both attempts, the check fails and the ALB pulls the task out of rotation after its own unhealthy_threshold_count consecutive failures. On final failure we return 503 directly via `JSONResponse` instead of raising `HTTPException`. The status to the ALB is identical, but the Sentry FastAPI integration only captures *exceptions* — so this path no longer triggers the "new unhandled error" PD rule on a transient blip. Sustained DB-unreachable is correctly surfaced by the ALB target-health alarm, not the Sentry new-issue rule.