[InputProcessor] Make external request_id optional

[markmc]

Perhaps we can do this as a follow-on, but it might be good to make the external req id optional so in the default case we can then have a more compact internal id.

We could then also avoid generating multiple uuids per request in the api server case.

Originally posted by @njhill in #27987 (comment)

[markmc]

Making request_id optional at the AsyncLLM level, then removing the UUID generation in the API server, and figuring out what to do about the per-endpoint prefix (e.g. "cmpl-")