feat(ui): implement public status endpoint and update UI components

* add public status handler and response types
* modify status API to restrict access and update client tracking
* adjust UI components to display public status information
* update routing to include public status endpoint

ui/vite.config.ts

@@ -11,6 +11,7 @@ export default defineConfig({
     port: 5173,
     proxy: {
       '/api': backendTarget,
+      '/status': backendTarget,
       '/healthz': backendTarget,
       '/readyz': backendTarget,
       '/llm': backendTarget,