[Core] Simplify and unify mm uuid handling & auto-generated mm hash overrides processing.

[huachenheli]

Purpose

Unify multimodal UUID & hash overrides logic.

After #23690 and #23394, when we auto-generate mm identifiers using f"{request_id}-{modality}-{i}" they effectively serve as uuids which also get hashed later on. So we don't need to track user-provided UUIDs and auto-generated ones (when caching is disabled) separately but rather can simplify the processing flow in a unified manner.

cc. @ywang96 @DarkLight1337

Test Plan

pytest tests/v1/engine/test_processor_multi_modal_uuids.py

CUDA_VISIBLE_DEVICES=0 python -m vllm.entrypoints.openai.api_server --model Qwen/Qwen2.5-VL-3B-Instruct --dtype bfloat16 --limit-mm-per-prompt '{"image":1, "video":1}' --mm_processor_cache_gb=0 --no-enable_prefix_caching with image queries

Test Result

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[mergify]

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

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

[mergify]

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

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

[DarkLight1337]

Makes sense, thanks!