[V0][Bugfix] Fix Mamba cache crashing

[benchislett]

When a request is finished but the scheduler has no more requests, the finished_req_ids will be cleared from the scheduler but the model execution will be skipped. This means that the Mamba cache cannot free the slots for those requests, leading to a slow buildup of unavailable slots until there are none left.

This PR changes the behaviour of the LLM engine to only clear the finished_req_ids when there are scheduled requests to process.

FIX #13129

[github-actions]

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[youkaichao]

@tlrmchlsmth is the expert on mamba

[tlrmchlsmth]

This looks good. It looks like the fix is already in async_llm_engine.py but not llm_engine.py, so please merge in latest main. (And please make sure the code is equivalent in the two files as well). Thank you!

[mergify]

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

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

[benchislett]

@tlrmchlsmth conflict resolved, diff looks good, ready to merge.

[sssrijan-amazon]

Is this change not going to be merged? Any updates?

[tlrmchlsmth]

@benchislett could you merge in latest main?