Migrate from Create React App to Vite

CRA (react-scripts 5.0.1) is abandoned and incompatible with TypeScript 5.x.
Vite provides faster builds, active maintenance, and native TS5 support.

- Replace react-scripts with vite + @vitejs/plugin-react
- Move index.html to root with script module entry point
- Replace setupProxy.js with vite.config.ts proxy config
- Rename env vars from REACT_APP_ to VITE_ prefix
- Update tsconfig for bundler module resolution
- Add nginx setup script for deployment

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/index.tsx

@@ -3,7 +3,7 @@ import ReactDOM from 'react-dom/client';
 import { LanguageProvider } from './contexts/LanguageContext';
 import App from './App';
 
-const root = ReactDOM.createRoot(document.getElementById('root'));
+const root = ReactDOM.createRoot(document.getElementById('root')!);
 root.render(
   <React.StrictMode>
     <LanguageProvider>