[router] refactor router and worker management 2/n (#10666)

sgl-router/tests/test_pd_routing.rs

@@ -207,19 +207,21 @@ mod test_pd_routing {
                 history_backend: sglang_router_rs::config::HistoryBackend::Memory,
             };
 
-            // Router creation will fail due to health checks, but config should be valid
             let app_context =
                 sglang_router_rs::server::AppContext::new(config, reqwest::Client::new(), 64, None)
                     .expect("Failed to create AppContext");
             let app_context = std::sync::Arc::new(app_context);
             let result = RouterFactory::create_router(&app_context).await;
-            assert!(result.is_err());
-            let error_msg = result.unwrap_err();
-            // Error should be about health/timeout, not configuration
             assert!(
-                error_msg.contains("healthy") || error_msg.contains("timeout"),
-                "Unexpected error: {}",
-                error_msg
+                result.is_ok(),
+                "Router creation should succeed with empty worker"
+            );
+
+            // Verify that no workers are registered since we didn't initialize them
+            let stats = app_context.worker_registry.stats();
+            assert_eq!(
+                stats.total_workers, 0,
+                "No workers should be registered without initialization"
             );
         }
     }