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

examples/storytelling-chatbot/client/app/utils.ts

@@ -0,0 +1,6 @@
+import { type ClassValue, clsx } from "clsx"
+import { twMerge } from "tailwind-merge"
+
+export function cn(...inputs: ClassValue[]) {
+  return twMerge(clsx(inputs))
+}