[Feat] Tool calling support for MCP client integration

[YuhanLiu11]

This PR adds support for tool calling in vLLM production stack, enabling MCP (Model Communication Protocol) clients and agents to work with models that support tools and functions. This is part of the ongoing work to optimize vLLM production-stack for agentic workflows as described in #244.

BEFORE SUBMITTING, PLEASE READ THE CHECKLIST BELOW AND FILL IN THE DESCRIPTION ABOVE

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• Make sure the code changes pass the pre-commit checks.
• Sign-off your commit by using -s when doing git commit
• Try to classify PRs for easy understanding of the type of changes, such as [Bugfix], [Feat], and [CI].

Detailed Checklist (Click to Expand)

Thank you for your contribution to production-stack! Before submitting the pull request, please ensure the PR meets the following criteria. This helps us maintain the code quality and improve the efficiency of the review process.

PR Title and Classification

Please try to classify PRs for easy understanding of the type of changes. The PR title is prefixed appropriately to indicate the type of change. Please use one of the following:

• [Bugfix] for bug fixes.
• [CI/Build] for build or continuous integration improvements.
• [Doc] for documentation fixes and improvements.
• [Feat] for new features in the cluster (e.g., autoscaling, disaggregated prefill, etc.).
• [Router] for changes to the vllm_router (e.g., routing algorithm, router observability, etc.).
• [Misc] for PRs that do not fit the above categories. Please use this sparingly.

Note: If the PR spans more than one category, please include all relevant prefixes.

Code Quality

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• Please include sufficient tests to ensure the change is stay correct and robust. This includes both unit tests and integration tests.

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, Shaoting-Feng or ApostaC.