[core] [2/N] refactor worker_base input preparation for multi-step

[SolitaryThinker]

small part of #7000

FIX #xxxx (link existing issues this PR will resolve)

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[github-actions]

👋 Hi! Thank you for contributing to the vLLM project.
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[SolitaryThinker]

/ready

[comaniac]

The refactor makes sense to me. LGTM

[zhuohan123]

LGTM!

[comaniac]

yapf failure is not related to this PR and should've been fixed in main branch. Merged.