[CI/Build][Doc] Fully deprecate old bench scripts for serving / throughput / latency

[yeqcharlotte]

Purpose

Follow up of #21355. Delete old benchmarks/benchmark_(latency|throughput|serving).py to avoid confusion for contributing into these scripts.

Given CI has been running on the new script for 1 month so far, it should be fine to delete these scripts.

Test Plan

Make sure no more references in: https://github.com/search?q=repo%3Avllm-project%2Fvllm+%2Fbenchmark_%28latency%7Cserving%7Cthroughput%29.py%2F&type=code

Test current output:

python benchmarks/benchmark_latency.py

Test Result

terminal shows it prints deprecation and exits 1

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Essential Elements of an Effective PR Description Checklist

• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model.
• (Optional) Release notes update. If your change is user facing, please update the release notes draft in the Google Doc.

[gemini-code-assist]

Code Review

This pull request effectively deprecates the old benchmark scripts (benchmark_latency.py, benchmark_serving.py, benchmark_throughput.py) by replacing their contents with a helpful message pointing to the new vLLM CLI commands. The documentation in benchmarks/README.md is also updated accordingly. My main feedback is to improve the deprecation scripts to exit with a non-zero status code and print to stderr, which is crucial for automation and CI/CD pipelines to correctly detect that the old scripts are no longer functional.

[mergify]

This pull request has merge conflicts that must be resolved before it can be
merged. Please rebase the PR, @yeqcharlotte.

https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/syncing-a-fork

[hmellor]

Maybe something for a follow up PR but could the content of this README be moved to docs/contributing/benchmarks.md? Right now the information about benchmarking in the docs is quite sparse and this README contains loads of useful information

[yeqcharlotte]

that's a good idea. possibly i can follow up with @ywang96 to see if we can take a more systematic approach about all these random benchmark scripts. :D

[hmellor]

LGTM!