[Misc] Minor refactoring for scheduler

[WoosukKwon]

This PR implements minor refactoring for the scheduler, preparing for #19970.
Since the PR only re-locates the existing code without functionality changes, the correctness and performance should not be affected.

[gemini-code-assist]

Summary of Changes

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This pull request focuses on refactoring the scheduler code in vllm/v1/core/sched/scheduler.py to improve its structure and readability. It involves moving code blocks into separate functions and optimizing iterations. The changes are intended to prepare the codebase for upcoming features without altering the existing functionality or performance.

Highlights

• Refactoring: The schedule function in vllm/v1/core/sched/scheduler.py is refactored to improve readability and prepare for future changes. The logic for updating the number of computed tokens is moved into a new function _update_after_schedule.
• Code Movement: The code block responsible for freeing encoder inputs is extracted into a new private method called _free_encoder_inputs and called from update_from_output.
• Optimization: The code now directly iterates over cached_encoder_input_ids instead of converting it to a list first, which avoids unnecessary memory allocation.

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[gemini-code-assist]

Code Review

The pull request effectively refactors parts of the Scheduler class by extracting logical blocks of code into new private methods. This improves the modularity and readability of the schedule and update_from_output methods without altering the core functionality or performance. The changes align well with the stated objective of minor refactoring.

[github-actions]

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