The API answers GET /v1/health/deep with 503 and a full report when a
dependency is down. _handle_response raised for every status at or above
400, so deep_health() raised exactly when callers need the dependency
details. Both the sync and async clients now accept 503 for this endpoint.
Claude-Session: https://claude.ai/code/session_01Agoc9bRVE9KL7mmWtey9Vq