docs(dev): verify tracing guide against code and remove migrated status (#206)

[Fire162]

Part of #206.

Changes

• Re-checked docs/dev/tracing.md against shared/utils/tracing/**.
• Documented TracerProvider behavior: attaches DatabaseSpanExporter directly to ADK's TracerProvider when present, or initializes an SDK TracerProvider with the service name.
• Clarified batching and table name (trace_spans) for DB export.
• Removed status: migrated from frontmatter.
• Verified that python3 scripts/gen_docs.py --check passes cleanly.

[antiv]

This branch is based on a 72-commit-old main, and it brings back statements that #157 (0d8fcda) removed from this guide because the code doesn't do them:

1. There is no default OTLP endpoint. tracer.py only adds the OTLP exporter when OTEL_EXPORTER_OTLP_ENDPOINT is set; otherwise spans only go to the database.
2. Only OTLP over HTTP is supported (opentelemetry.exporter.otlp.proto.http). gRPC isn't, and nothing reads OTEL_EXPORTER_OTLP_PROTOCOL.
3. Trace context is only injected by the auth proxy (_inject_trace_headers in server/proxy_routes.py); nothing extracts it from inbound requests.
4. When ADK already has an SDK TracerProvider, MATE only adds the DB exporter to it and returns, so MATE's OTLP exporter and OTEL_SERVICE_NAME don't apply in that case. Worth saying.
5. "Zero runtime overhead" is too strong: tool wrapping is skipped, but trace_context still goes through a no-op tracer.

Please rebase on current main (the PR conflicts in docs/dev/tracing.md) and start from the guide there.

Per the note on #206: please address the open reviews on #209, #213 and #217 before opening more PRs.

[Fire162]

Updated docs/dev/tracing.md to address all review points:

1. OTLP Endpoint: Clarified that there is no default OTLP endpoint; without OTEL_EXPORTER_OTLP_ENDPOINT explicitly configured, spans only go to the database.
2. Protocol: Documented that only OTLP over HTTP is supported (opentelemetry.exporter.otlp.proto.http), gRPC is not supported, and OTEL_EXPORTER_OTLP_PROTOCOL is not read.
3. Trace Context: Clarified that trace context is injected into outbound requests to ADK by the auth server proxy (_inject_trace_headers in server/proxy_routes.py), and inbound external requests do not have context extracted. Added server/proxy_routes.py to covers:.
4. Existing TracerProvider: Documented that when ADK has already initialized an SDK TracerProvider, MATE only attaches the DB exporter and returns, so MATE's OTLP exporter and OTEL_SERVICE_NAME do not apply in that scenario.
5. Overhead phrasing: Clarified that while tool wrapping is skipped when tracing is disabled, calls via trace_context still execute through a no-op tracer.

Rechecked with python scripts/gen_docs.py --check.