#2659 Document Gateway trace context and baggage forwarding

Summary

Documents the behavior added to the AI Gateway. The Gateway continues the caller's trace from traceparent, and copies baggage entries onto the span it records in the project.

• New page docs/reference/advanced/gateway/telemetry.md, "See Gateway requests in your app's trace". It covers prerequisites, a Pydantic AI setup and an OpenAI SDK setup, a verify step with a SQL query, what the Gateway does with each header, and troubleshooting.
• gateway/index.md: the ### Telemetry section now names the Include messages setting as the UI shows it and links to the new page.
• navigation.yml: adds the page to the AI Gateway section after "Send Your First Request".
• baggage.md: one sentence that links to the new page.

The page is a new how-to rather than a longer Telemetry section, so the overview stays short and each page does one job.

Validation

• uv run pytest tests/test_docs.py tests/test_docs_serve.py: 269 passed. Both Python examples are tagged skip-run with external-connection, as the other Gateway examples are. Two runs reported 2 failures that did not reproduce in five reruns, and I did not capture which tests they were.
• prek run on the changed files passes.
• End-to-end run. I ran the two code blocks from this page, extracted from the Markdown, against a local Gateway with a fake OpenAI upstream and a local collector standing in for Logfire. Results:
  • Pydantic AI: the Gateway span is a child of the chat gpt-5.2 span, in the same trace. user_tier, experiment, and Pydantic AI's own gen_ai.agent.name, gen_ai.agent.call.id and gen_ai.conversation.id appear as attributes on the Gateway span. This works without instrument_httpx, because Pydantic AI's gateway/ provider sends the headers itself.
  • OpenAI SDK with instrument_httpx: the Gateway span is a child of the POST span. Without instrument_httpx it starts a trace of its own.
  • The fake upstream received exactly one traceparent carrying the client's trace id, and no baggage header.
  • With Include messages off, a baggage entry named gen_ai.input.messages is not copied as an attribute. The whole header is still recorded as http.request.header.baggage, and the page says so.