Add proper readiness checks to health interceptor

[smoreinis]

Summary

• Separates liveness (/healthz) from readiness (/readyz, /healthcheck) probes
• Liveness probe returns 200 immediately (sub-millisecond) without checking dependencies
• Readiness probes check PostgreSQL, Redis, and MongoDB connectivity
• Returns 503 with detailed status when dependencies are unhealthy or not initialized
• Adds per-check timeout (2s) and overall timeout (5s) to prevent hung health checks

Why this matters

Previously, all health check paths returned 200 regardless of dependency health. This meant Kubernetes would continue routing traffic to pods that couldn't actually serve requests. Now:

• /healthz (liveness): Fast response for Kubernetes to detect stuck processes
• /readyz and /healthcheck (readiness): Actual dependency validation before accepting traffic

Response format (readiness)

{
  "status": "ok",  // or "degraded"
  "checks": {
    "postgres": {"healthy": true},
    "redis": {"healthy": true},
    "mongodb": {"healthy": true}
  }
}

Test plan

• Unit tests verify liveness returns 200 without checking deps
• Unit tests verify readiness returns 503 when deps unavailable
• Unit tests verify readiness returns 200 when all deps healthy
• All 188 unit tests pass