[router] Basic OAI Response api (#10346)

sgl-router/src/routers/mod.rs

@@ -9,7 +9,9 @@ use axum::{
 };
 use std::fmt::Debug;
 
-use crate::protocols::spec::{ChatCompletionRequest, CompletionRequest, GenerateRequest};
+use crate::protocols::spec::{
+    ChatCompletionRequest, CompletionRequest, GenerateRequest, ResponsesRequest,
+};
 
 pub mod factory;
 pub mod grpc;
@@ -78,6 +80,13 @@ pub trait RouterTrait: Send + Sync + Debug + WorkerManagement {
         body: &CompletionRequest,
     ) -> Response;
 
+    /// Route a responses request
+    async fn route_responses(
+        &self,
+        headers: Option<&HeaderMap>,
+        body: &ResponsesRequest,
+    ) -> Response;
+
     async fn route_embeddings(&self, headers: Option<&HeaderMap>, body: Body) -> Response;
 
     async fn route_rerank(&self, headers: Option<&HeaderMap>, body: Body) -> Response;