[V1] Make AsyncLLMEngine v1-v0 opaque

[rickyyx]

Right now, users of the AsyncLLMEngine will have to modify their code to use V1 even if VLLM_USE_V1=1 is used.

We should have the V1/V0 behaviour changed by VLLM_USE_V1 sorely as much as possible.

[github-actions]

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

LGTM. cc @WoosukKwon @robertgshaw2-neuralmagic

[rickyyx]

Test failures look unrelated on AMD.