feat(webui): add PWA support for mobile home screen installation

- Add manifest.json with icons for install prompt
- Add service worker with cache-first for static assets
- Register SW in main.tsx
- Link manifest in index.html

webui/src/main.tsx

@@ -28,3 +28,11 @@ initializeLoopbackRuntimeHost();
 
 /* StrictMode disabled: dev double-invokes state updaters; delta accumulation must stay pure — see useNanobotStream. */
 ReactDOM.createRoot(root).render(<App />);
+
+if ("serviceWorker" in navigator) {
+  window.addEventListener("load", () => {
+    navigator.serviceWorker.register("/sw.js", {
+      updateViaCache: "none",
+    });
+  });
+}