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>

tsconfig.json

@@ -11,12 +11,13 @@
     "strictNullChecks": false,
     "forceConsistentCasingInFileNames": true,
     "noFallthroughCasesInSwitch": true,
-    "module": "esnext",
-    "moduleResolution": "node",
+    "module": "ESNext",
+    "moduleResolution": "bundler",
     "resolveJsonModule": true,
     "isolatedModules": true,
     "noEmit": true,
-    "jsx": "react-jsx"
+    "jsx": "react-jsx",
+    "types": ["vite/client"]
   },
   "include": ["src"]
 }