[Feature] request for "classify" method for sglang router

Checklist

• If this is not a feature request but a general question, please start a discussion at https://github.com/sgl-project/sglang/discussions. Otherwise, it will be closed.
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Motivation

In RL, we may launch a router to dispatch reward computation requests for both generative rewards (via /generate) and discriminative rewards (via /classify). I note that the "classify" api has not been implemented in sglang router (https://docs.sglang.io/advanced_features/router.html#api-surface). Hope future release will include this feat.

In addition to this, I want to report a bug that in the latest sglang router, the router fails to handle "v1/embeddings" requests after the servers sleep and then wake up.

# step 1: Launch multiple workers and one router
# step 2: Sleep servers and then wake up them
# step 3: Post "v1/embeddings" requests to router

For sglang-router==0.2.4 curl http://{router_address}/v1/models {"object":"list","data":[{"id":"unknown","object":"model","owned_by":"local"}]} and the reward computation also fails

For sglang-router==0.2.2 all behaviors are correct

@slin1237 @zhaochenyang20

Related resources

No response