feat: update frontend for four-tier role system

Add Student Admin and Teacher Admin roles to constants, types, store,
permissions, routes, and admin UI. Teacher Admin sees contests and
problemsets in sidebar; Student Admin sees only problems.

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

src/shared/components/Header.vue

@@ -166,7 +166,7 @@ const menus = computed<MenuOption[]>(() => [
     label: () =>
       h(
         RouterLink,
-        { to: userStore.isTheAdmin ? "/admin/problem/list" : "/admin" },
+        { to: userStore.isSuperAdmin ? "/admin" : "/admin/problem/list" },
         { default: () => "后台" },
       ),
     show: userStore.isAdminRole,