[Refactor] Get prompt updates earlier

[DarkLight1337]

Purpose

More refactoring to enable #23018

• Get prompt updates inside _apply_hf_processor
• Conbine mm_kwargs, mm_hashes, mm_prompt_updates in the return value of _apply_hf_processor into a single tuple for brevity

Test Plan

Test Result

(Optional) Documentation Update

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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.

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[gemini-code-assist]

Code Review

This pull request refactors the multimodal processing logic to compute prompt updates earlier in the pipeline. This is achieved by introducing a MultiModalProcessingInfo data class to bundle mm_kwargs, mm_hashes, and mm_prompt_updates, and moving the prompt update creation into _apply_hf_processor and _cached_apply_hf_processor. The changes are well-structured and improve the code's clarity.

I've found one critical issue in qwen2_5_omni_thinker.py where the logic for determining use_audio_in_video seems to be incorrect due to the use of &= instead of =. Please see my detailed comment.