[Feature]: Consolidate benchmark_serving.py and serve.py to avoid code duplication and usage confusions

[Jialin]

🚀 The feature, motivation and pitch

Currently, we have 2 versions of benchmark scripts (e.g. benchmark_serving.py and serve.py). Most of their code are simply duplicated, and sometime it's confusing which should be treated as the source of truth.

Discussed with @simon-mo @ywang96 @yeqcharlotte in #21108 (comment), we all agreed that we should ultimately deprecate benchmark_serving.py and only maintain serve.py as the golden benchmark script.

A few action items to address the issue.

• Stop refering benchmark_serving.py in all documentations
• Delete duplicated code in benchmark_serving.py, and reuse serve.py code as much as possible
• [Stretched] Delete benchmark_serving.py

Alternatives

No response

Additional context

No response

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[Jialin]

Thanks @yeqcharlotte to address this!