demo: Restructure storytelling-chatbot directory, update README steps, link to vercel demo

examples/storytelling-chatbot/client/next.config.mjs

@@ -0,0 +1,15 @@
+/** @type {import('next').NextConfig} */
+const nextConfig = {
+  output: "export",
+
+  async rewrites() {
+    return [
+      {
+        source: "/:path*",
+        destination: "http://localhost:7860/:path*",
+      },
+    ];
+  },
+};
+
+export default nextConfig;