feat(obs): distributed traces across the .NET services (S-16b, closes #123) (#126)

## What & why

S-16b, second of the S-16 split, on top of the #125 backplane. The five .NET services now emit OpenTelemetry traces so a request is **one connected trace** across them.

- Each host wires `AddOpenTelemetry().WithTracing(...)` with `AddAspNetCoreInstrumentation` (incoming) + `AddHttpClientInstrumentation` (outgoing) + `AddOtlpExporter` to **Tempo**.
- Because every cross-service call already goes through a typed `HttpClient` (§8 boundaries), the W3C `traceparent` propagates with no manual code — bff → domain → acl → openzaak and bff → projection-api stitch into a single trace.
- Service name + OTLP endpoint come from `OTEL_*` env set per app service in compose. `/health` is filtered out so liveness polls don't flood the traces.

No new ADR — ADR-0023 already records the stack + the two documented gaps (browser-side tracing is out of scope, so the trace begins at the BFF; the async Flowable-poll boundary is a separate trace).

Closes #123

## Definition of Done

- [x] Failing test committed first (`verify-tracing` fails with no instrumentation).
- [x] Implementation makes it pass — **validated locally end to end**: a real connected trace spanning `bff` + `projection-api` was found in Tempo (BFF→projection→db + Tempo subset, no OpenZaak/egress).
- [x] Conventional Commits referencing the issue (`refs #123`).
- [ ] CI green — awaiting Gitea Actions (verify-tracing added to verify-stack after verify-bff).
- [x] `docker compose up` health unaffected — services boot healthy even when Tempo is unreachable (exporter no-ops; verified).
- [x] Docs — demo-script + BACKLOG.
- [x] ADR — none needed (covered by ADR-0023).

## Notes for reviewers

- **Per-service wiring, no shared lib:** the block is duplicated across the five hosts by design — services don't share code across boundaries here (§8), same as the duplicated typed clients.
- **Packages:** OpenTelemetry.Extensions.Hosting / Instrumentation.AspNetCore / Instrumentation.Http / Exporter.OpenTelemetryProtocol, all 1.17.0, pinned per-csproj (no central props file).
- **The check** generates anonymous BFF→projection traffic (no auth, no OpenZaak), then queries Tempo (TraceQL search → fetch trace → assert both service.names present) from a python:3-slim container in-network — same idiom as run-projection-check.sh.
- **Next:** #124 (S-16c) adds `/metrics` + Prometheus scrape targets + golden-signal Grafana dashboards.

Reviewed-on: #126

docs/demo-script.md

@@ -5,6 +5,33 @@ copy-pasteable walkthrough against a local `make up` stack.
 
 ---
 
+## S-16b — distributed traces across the .NET services (#123, ADR-0023)
+
+**Outcome:** the five .NET services (BFF, Domain, ACL, projection-api, event-subscriber) now emit
+OpenTelemetry traces — ASP.NET Core + `HttpClient` auto-instrumentation, exported over OTLP to Tempo.
+Because every cross-service call goes through a typed `HttpClient`, the W3C `traceparent` propagates for
+free, so a request is **one connected trace** across the services (bff → domain → acl → openzaak;
+bff → projection-api). `/health` is filtered out. No browser-side instrumentation yet, so the trace
+begins at the BFF; the async Flowable-poll boundary is a separate trace (ADR-0023).
+
+```bash
+# 1. Automated (a CI verify-stack step): generate BFF traffic and assert Tempo holds one trace
+#    spanning multiple services.
+make verify-tracing              # → OK — trace <id> spans ['bff', 'projection-api']
+
+# 2. By hand: drive the stack, then explore traces in Grafana.
+make up
+curl -s localhost:8080/openbaar/register >/dev/null   # BFF → projection-api
+open http://localhost:3000       # Grafana → Explore → Tempo → Search → service.name = bff → open a trace
+```
+
+**The path:** each host wires `AddOpenTelemetry().WithTracing(AddAspNetCoreInstrumentation +
+AddHttpClientInstrumentation + AddOtlpExporter)`; `OTEL_SERVICE_NAME` / `OTEL_EXPORTER_OTLP_ENDPOINT`
+come from compose; spans export to **tempo:4317** and render in Grafana against the provisioned Tempo
+datasource.
+
+---
+
 ## S-16a — observability backplane: Tempo + Prometheus + Grafana (#122, ADR-0023)
 
 **Outcome:** the compose stack now includes a Grafana-native observability backplane — **Tempo** (OTLP