feat: complete TASK-WP0-06 public cache

apps/web/src/main.tsx

@@ -2,6 +2,7 @@ import { StrictMode } from "react";
 import { createRoot } from "react-dom/client";
 
 import { ToolchainProbe } from "./toolchain-probe.js";
+import { registerPublicAssetServiceWorker } from "./public-asset-cache.js";
 
 const root = document.getElementById("root");
 
@@ -9,6 +10,9 @@ if (!root) {
   throw new Error("Dada web root element is missing.");
 }
 
+// Cache failure leaves public assets network-backed and must not create alternate persistence.
+void registerPublicAssetServiceWorker().catch(() => undefined);
+
 createRoot(root).render(
   <StrictMode>
     <ToolchainProbe />