feat(readiness-probe-improvements): AIPLAT-916

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Jira ticket: AIPLAT-916
Infra PR companion should be merged first: https://github.com/mozilla/dataservices-infra/pull/2090

What's New

/health/readiness now answers "can this pod serve a request right now?" via the HTTP status code, instead of always returning 200.

Kubernetes routes on the status code, so a pod with a down Postgres pool or a stale app_attest schema now drains from rotation instead of serving 500s.

Three checks run concurrently (asyncio.gather), each bounded by READINESS_CHECK_TIMEOUT_S (2s). All pass -> 200; any fail -> 503 with the failing check named in the body:

1. litellm pool: real SELECT 1 (replaces the old _closed-flag read, which only knew if .close() was called).
2. app_attest pool + migration head: reads alembic_version and asserts it equals the Alembic head(s) the running code ships. The read doubles as the pool's liveness check.
3. LiteLLM readiness: requires HTTP 200 and db == "connected" (the old code parsed the body but never checked the status, so a 503-with-body read as healthy).

Liveness stays a constant {"status": "alive"}, so a dependency blip drains the pod without ever restarting it, no crash-loop path from this change.

QA:

all new unit tests ✅