[Renderer] Deprecate code paths for old input processing

[DarkLight1337]

Purpose

Follow-up to #34560

Encourage people to use Renderer code path instead of applying preprocessing inside InputProcessor.

Test Plan

Test Result

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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.
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[gemini-code-assist]

Code Review

This pull request deprecates old input processing code paths, encouraging the use of the Renderer for preprocessing. The changes are consistent and well-aligned with this goal, removing tokenization_kwargs from several internal functions and adding clear deprecation warnings for old APIs. However, I've identified a high-severity issue in the backward compatibility implementation for Platform.validate_request which could break custom platform implementations. My review includes suggestions to fix this while preserving the intended deprecation path.

[mergify]

Documentation preview: https://vllm--34775.org.readthedocs.build/en/34775/