POL-124: Migrate frontend from React Native to Next.js web app

- Replace mobile/ (Expo) with web/ (Next.js 16 + Tailwind + shadcn/ui)
- Pages: login, register, pending, championships, championship detail, registrations, profile, admin
- Logic/view separated: hooks/ for data, components/ for UI, pages compose both
- Types in src/types/ (one interface per file)
- Auth: Zustand store + localStorage tokens + cookie presence flag for proxy
- API layer: axios client with JWT auto-refresh

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

web/src/app/(auth)/layout.tsx

@@ -0,0 +1,7 @@
+export default function AuthLayout({ children }: { children: React.ReactNode }) {
+  return (
+    <div className="flex min-h-screen items-center justify-center bg-gradient-to-br from-violet-50 to-purple-100 p-4">
+      <div className="w-full max-w-md">{children}</div>
+    </div>
+  );
+}