feat(observability): Prometheus metrics for HTTP requests

[chitrank2050]

Problem

No runtime metrics exist. We can't answer: "what's our API latency?", "how many 5xx errors per minute?", "which endpoints are slowest?"

Proposed solution

Integrate prom-client with NestJS:

1. GET /metrics endpoint exposing Prometheus-format metrics
2. Default metrics: Node.js process stats (memory, CPU, event loop lag)
3. HTTP request metrics via middleware:
   • http_request_duration_seconds (histogram) — labeled by method, path, status
   • http_requests_total (counter) — labeled by method, path, status
   • http_active_requests (gauge) — currently in-flight requests
4. Path normalization: /invoices/uuid → /invoices/:id (prevents high-cardinality labels)

API design

GET /metrics
→ 200
Content-Type: text/plain
"/api/v1/entitlements/:featureKey/check"

Alternatives considered

• StatsD — rejected. Prometheus pull model is simpler for Kubernetes deployments.
• Custom metrics endpoint — rejected. Prometheus format is the industry standard. Every monitoring stack supports it.

Additional context

prom-client is the standard Node.js Prometheus library. Install via pnpm add prom-client.