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/package.json

@@ -0,0 +1,36 @@
+{
+  "name": "web",
+  "version": "0.1.0",
+  "private": true,
+  "scripts": {
+    "dev": "next dev",
+    "build": "next build",
+    "start": "next start",
+    "lint": "eslint"
+  },
+  "dependencies": {
+    "@tanstack/react-query": "^5.90.21",
+    "axios": "^1.13.5",
+    "class-variance-authority": "^0.7.1",
+    "clsx": "^2.1.1",
+    "lucide-react": "^0.575.0",
+    "next": "16.1.6",
+    "radix-ui": "^1.4.3",
+    "react": "19.2.3",
+    "react-dom": "19.2.3",
+    "tailwind-merge": "^3.5.0",
+    "zustand": "^5.0.11"
+  },
+  "devDependencies": {
+    "@tailwindcss/postcss": "^4",
+    "@types/node": "^20",
+    "@types/react": "^19",
+    "@types/react-dom": "^19",
+    "eslint": "^9",
+    "eslint-config-next": "16.1.6",
+    "shadcn": "^3.8.5",
+    "tailwindcss": "^4",
+    "tw-animate-css": "^1.4.0",
+    "typescript": "^5"
+  }
+}