Split health checks into liveness and readiness endpoints

[Subhransu-De]

What to build

Replace the single database health endpoint with production-oriented liveness and readiness checks. Liveness should answer whether the process is alive. Readiness should answer whether it is safe to receive traffic.

Acceptance criteria

• /health/live returns success without depending on the database.
• /health/ready checks database connectivity.
• Existing /health/db is either retained as a compatibility alias or deprecated intentionally.
• Docker healthcheck and docs use the appropriate endpoint.
• Tests cover live and ready behavior.

Blocked by

None - can start immediately.