Observability: structured logs, metrics, tracing

[mondial7]

Today logging is stdlib log to stdout. Nothing else.

Scope

• Structured logging (zap or slog) with request IDs propagated via Gin middleware.
• Prometheus /metrics endpoint (request count, latency histograms, Mongo round-trip times, Gemini call duration / failure rate).
• OpenTelemetry tracing — at least HTTP → Mongo → Gemini spans.
• Sample Grafana dashboard JSON checked into docs/.
• Alerting recipes (error rate, p95 latency, Gemini quota approaching).

Effort: medium-large (4–5 days).

[mondial7]

Partly delivered in #57: structured logging (slog, LOG_FORMAT=text|json) and a live log-stream — an in-memory hub feeding an admin Logs page over SSE, plus JSON-to-shipper on stdout. Still open: metrics and distributed tracing (e.g. Prometheus/OpenTelemetry). Suggest narrowing this issue to metrics + tracing.