feat: enhance sport selection UI in public booking page

Co-authored-by: Copilot <copilot@github.com>

apps/frontend/package.json

@@ -15,10 +15,12 @@
     "@better-auth/infra": "^0.2.4",
     "@fontsource-variable/geist": "^5.2.8",
     "@hookform/resolvers": "^5.2.2",
+    "@phosphor-icons/react": "^2.1.10",
     "@radix-ui/react-label": "^2.1.8",
     "@radix-ui/react-popover": "^1.1.2",
     "@radix-ui/react-slot": "^1.2.4",
     "@repo/api-contract": "workspace:*",
+    "@tabler/icons-react": "^3.41.1",
     "@tanstack/react-query": "^5.96.1",
     "@tanstack/react-query-devtools": "^5.96.1",
     "@tanstack/react-router": "^1.168.10",