[Observability AI] Add Observability to vLLM docs

[mdbirnstiehl]

Summary

This PR closes #5347 and updates the Connect to vLLM docs to include Observability use cases.

Generative AI disclosure

1. Did you use a generative AI (GenAI) tool to assist in creating this contribution?

• Yes
• No

2. If you answered "Yes" to the previous question, please specify the tool(s) and model(s) used (e.g., Google Gemini, OpenAI ChatGPT-4, etc.).

Tool(s) and model(s) used: Claude code