feat: initialize Convert UI - browser-based file conversion app

- Add Next.js 16 with Turbopack and React 19
- Add Tailwind CSS 4 with OKLCH color system
- Implement FFmpeg.wasm for video/audio conversion
- Implement ImageMagick WASM for image conversion
- Add file upload with drag-and-drop
- Add format selector with fuzzy search
- Add conversion preview and download
- Add conversion history with localStorage
- Add dark/light theme support
- Support 22+ file formats across video, audio, and images

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

app/page.tsx

@@ -0,0 +1,69 @@
+'use client';
+
+import { FileConverter } from '@/components/converter/FileConverter';
+import { ThemeToggle } from '@/components/layout/ThemeToggle';
+import { ToastProvider } from '@/components/ui/Toast';
+
+export default function Home() {
+  return (
+    <ToastProvider>
+      <div className="min-h-screen bg-background">
+        {/* Header */}
+        <header className="border-b border-border">
+          <div className="container mx-auto px-4 py-4 flex items-center justify-between">
+            <div>
+              <h1 className="text-2xl font-bold text-foreground">Convert UI</h1>
+              <p className="text-sm text-muted-foreground">
+                File conversion in your browser
+              </p>
+            </div>
+            <ThemeToggle />
+          </div>
+        </header>
+
+        {/* Main content */}
+        <main className="container mx-auto px-4 py-8 md:py-16">
+          <FileConverter />
+        </main>
+
+        {/* Footer */}
+        <footer className="border-t border-border mt-16">
+          <div className="container mx-auto px-4 py-6 text-center text-sm text-muted-foreground">
+            <p>
+              Powered by{' '}
+              <a
+                href="https://github.com/ffmpegwasm/ffmpeg.wasm"
+                target="_blank"
+                rel="noopener noreferrer"
+                className="text-primary hover:underline"
+              >
+                FFmpeg.wasm
+              </a>
+              ,{' '}
+              <a
+                href="https://github.com/dlemstra/magick-wasm"
+                target="_blank"
+                rel="noopener noreferrer"
+                className="text-primary hover:underline"
+              >
+                ImageMagick WASM
+              </a>
+              {' '}&{' '}
+              <a
+                href="https://nextjs.org"
+                target="_blank"
+                rel="noopener noreferrer"
+                className="text-primary hover:underline"
+              >
+                Next.js 16
+              </a>
+            </p>
+            <p className="mt-2">
+              All conversions happen locally in your browser. No files are uploaded to any server.
+            </p>
+          </div>
+        </footer>
+      </div>
+    </ToastProvider>
+  );
+}