[sgl-router] Render chat prompts with dynamo-render (#38983)

Co-authored-by: Claude Fable 5.1 <noreply@anthropic.com>

experimental/sgl-router/tests/component/discovery/static_urls.rs

@@ -130,6 +130,7 @@ async fn static_urls_pd_role_resolved_end_to_end() {
         model: sgl_router::config::ModelConfig {
             id: "tiny".into(),
             tokenizer_path: "tests/fixtures/tiny_tokenizer.json".into(),
+            disable_input_ids_forwarding: false,
             policy: sgl_router::config::PolicyKind::RoundRobin,
             decode_policy: Default::default(),
             bucket_config: None,