[llm][docs] Restore literalinclude to code example

[eicherseiji]

Description

Fix documentation regression introduced in #57787 where the prefix-aware routing example used incorrect kwargs.
This PR restores the literalinclude directive that references the tested example file, ensuring the documentation stays in sync with the actual API and CI validates the example.

Related issues

Fixes regression from #57787

Additional information

Before (incorrect):

app = build_openai_app({
    "llm_configs": [llm_config],
    "router_cls": PrefixCacheAffinityRouter,  # Does not exist
    "router_config": {...}  # Does not exist
})

After (correct, via literalinclude):

llm_config = LLMConfig(
    ...
    deployment_config={
        ...
        "request_router_config": {
            "request_router_class": PrefixCacheAffinityRouter,
            "request_router_kwargs": {...},
        },
    },
)
app = build_openai_app({"llm_configs": [llm_config]})

[gemini-code-assist]

Code Review

This pull request fixes a regression in the documentation for prefix-aware routing. The incorrect, hardcoded code example has been replaced with a literalinclude directive. This is an excellent change as it ensures the documentation's code example is sourced directly from a tested file, preventing future discrepancies. The change is correct and improves the maintainability of the documentation.