Add animated rotating conical gradient background

- Create large 500% conical gradient with pastel color cycle
- Position gradient off-screen (-200% top/left) for smooth rotation
- Add 8s linear infinite rotation animation for fast testing
- Use ::before pseudo-element to avoid repainting main content
- Cycle through various pastel shades (pink, purple, blue, green, yellow, orange)
- Performance-optimized: only transforms, no gradient repainting

examples/chat-ui/src/components/ChatApp.tsx

@@ -102,7 +102,7 @@ const ChatApp: React.FC<ChatAppProps> = () => {
   };
 
   return (
-    <div className="flex h-dvh w-screen overflow-clip bg-gradient-to-br from-pink-100 via-purple-50 to-indigo-100">
+    <div className="flex h-dvh w-screen overflow-clip animated-gradient-bg">
       <div className="flex flex-row flex-grow flex-1 overflow-hidden relative">
         {/* Sidebar and Navbar components hidden but kept in codebase */}
         {false && (