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>

vite.config.ts

@@ -0,0 +1,18 @@
+import { defineConfig } from 'vite';
+import react from '@vitejs/plugin-react';
+
+export default defineConfig({
+  plugins: [react()],
+  server: {
+    port: 3000,
+    proxy: {
+      '/api': {
+        target: 'http://localhost:8090',
+        changeOrigin: true,
+      },
+    },
+  },
+  build: {
+    outDir: 'build',
+  },
+});