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/main.ts

@@ -40,7 +40,9 @@ router.beforeEach(async (to, from, next) => {
   if (
     to.matched.some(
       (record) =>
-        record.meta.requiresSuperAdmin || record.meta.requiresProblemPermission,
+        record.meta.requiresSuperAdmin ||
+        record.meta.requiresTeacherAdmin ||
+        record.meta.requiresProblemPermission,
     )
   ) {
     if (!storage.get(STORAGE_KEY.AUTHED)) {
@@ -63,6 +65,13 @@ router.beforeEach(async (to, from, next) => {
         next("/")
         return
       }
+    } else if (
+      to.matched.some((record) => record.meta.requiresTeacherAdmin)
+    ) {
+      if (!userStore.isTeacherOrAbove) {
+        next("/")
+        return
+      }
     } else if (
       to.matched.some((record) => record.meta.requiresProblemPermission)
     ) {