Real liveness probe. [LNK-OPSHEALTH]

This used to return {"status": "healthy", "timestamp": "2024-11-10T12:00:00Z"} — a hardcoded string that checked nothing and could not fail. deploy.sh gates the deploy on it, so a deploy that broke the database still reported success, and on 2026-08-15 a disk-full Postgres outage ran for three days while every surface above it looked healthy.

Contract:

• 503 when the database is unreachable — this is what makes curl -fsS in deploy.sh a real gate.
• 200 with a warning when disk is low. A full disk is serious but failing the deploy on it would block the very deploy that might fix it.