vLLM model handler efficiency improvements

[damccorm]

Because of how vLLM does batching, it is much more efficient if you're able to push as many requests to it as possible so that it can make the appropriate batching decision. Right now, per worker thread we send requests serially; this fixes that inefficiency by sending all data asynchronously to the vLLM server and then awaiting the response.

Fixes #32528

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