[MLOB-2411] Add Distributed Proxy/Gateway Service Guide for LLM Observability

[sabrenner]

What does this PR do? What is the motivation?

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Additional notes

[github-actions]

Preview links (active after the build_preview check completes)

New or renamed files

• https://docs-staging.datadoghq.com/sabrenner/llmobs-proxy-service-quickstart-guide/llm_observability/trace_proxy_services

Modified Files

• https://docs-staging.datadoghq.com/sabrenner/llmobs-proxy-service-quickstart-guide/llm_observability/guide/

[buraizu]

Created DOCS-10979 for documentation team review

[barieom]

Thanks Sam, this is looking great! Can we also add a section with one paragraph under Advanced Tracing? https://docs.datadoghq.com/llm_observability/setup/sdk/python/#advanced-tracing

[barieom]

Suggested change

	Like any traditionally application, LLM applications can be implemented across multiple different microservices. With LLM Observability, if one of these services is a LLM proxy or gateway service, you can trace the LLM calls made by individual LLM applications in a complete end-to-end trace.
	Like any traditional application, LLM applications can be implemented across multiple different microservices. With LLM Observability, if one of these services is an LLM proxy (or an LLM gateway service), you can trace the LLM calls made by individual LLM applications in a complete end-to-end trace that captures the full request path that jumps across multiple services.

[barieom]

Suggested change

	When making requests to the proxy or gateway service, the LLM Observability SDKs automatically propagate the ML application name from the original LLM application. The propagated ML application name takes precedence over the ML application name specified in the proxy or gateway service.
	When making requests to the proxy or gateway service, the LLM Observability SDK automatically propagates the ML application name from the original LLM application. The propagated ML application name takes precedence over the ML application name specified in the proxy or gateway service.