[ray.serve.llm] Fix setting up AutoProcessor

[GeneDer]

Why are these changes needed?

Was doing an end to end test and found out a different AutoProcessor was set on the vllm engine start vs used in the vlllm deployment. Remove the deep copy on llm_config during constructing of the vllm engine and moved set_processor call into apply_checkpoint_info. Also start to use real vllm engine in testing_model which is used by test_openai_compatibility.py to catch those types of issues.

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[GeneDer]

Seeing this working end2end in a workspace

[kouroshHakha]

LGTM