feat: initialize app with routing, query management, and UI framework

- Replace Vite boilerplate with React Router for page navigation
- Add React Query for server state and cache management
- Integrate shadcn/ui component library with Tailwind CSS v4
- Configure @/ path alias for clean module imports
- Set up Vite dev proxy to API backend
- Remove default App.css, App.tsx, and react.svg assets

src/lib/utils.ts

@@ -0,0 +1,6 @@
+import { clsx, type ClassValue } from "clsx"
+import { twMerge } from "tailwind-merge"
+
+export function cn(...inputs: ClassValue[]) {
+  return twMerge(clsx(inputs))
+}