[Feat][Doc] Add a load_balance_dp_proxy in examples and external dp doc.

[whx-sjtu]

What this PR does / why we need it?

This PR adds a load-balance dp proxy server which can be used in external DP scenario without Disaggregated-Prefill enabled. What's more, add a doc of external dp and load-balance dp proxy server.

Does this PR introduce any user-facing change?

No

How was this patch tested?

See the new doc.

• vLLM version: v0.11.0
• vLLM main: vllm-project/vllm@2918c1b

[github-actions]

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[gemini-code-assist]

Code Review

This PR introduces a load-balancing proxy for external data parallelism and adds corresponding documentation. The implementation of the proxy server has a critical issue with request body handling that will cause it to fail, and a high-severity issue where the load balancing metric is based on request body size instead of prompt token count, which could lead to suboptimal balancing. The documentation and examples also contain some incorrect filenames that should be fixed. I've provided suggestions to address these points.

[gemini-code-assist]

The load balancing logic currently uses request_length = len(req_body), which is the byte size of the entire JSON request body. This is not an accurate measure of the load, which is primarily determined by the number of tokens in the prompt. A request with a short prompt but large metadata could be incorrectly assessed as larger than a request with a long prompt.

To improve accuracy, you should estimate the number of tokens from the prompt text. You can access the prompt from req_data. A simple heuristic is to use the length of the prompt string.

        prompt_text = ""
        if api == "/completions":
            prompt = req_data.get("prompt")
            if isinstance(prompt, str):
                prompt_text = prompt
            elif isinstance(prompt, list):
                prompt_text = "".join(map(str, prompt))
        elif api == "/chat/completions":
            messages = req_data.get("messages", [])
            prompt_text = "\n".join(m.get("content", "") for m in messages if m.get("content"))

        # Using prompt length as a better heuristic for load.
        request_length = len(prompt_text)
        instance_info = await _select_instance(api, req_data,
                                                      request_length)

[whx-sjtu]

Please help me review the mooncake-related modifications of run_dp_template.sh @liziyu179