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/utils/functions.ts

@@ -133,15 +133,22 @@ export function debounce<T extends (...args: any[]) => any>(
 }
 
 export function getUserRole(role: User["admin_type"]): {
-  type: "default" | "info" | "error"
-  label: "普通" | "管理员" | "超管"
+  type: "default" | "info" | "warning" | "error"
+  label: "普通" | "学生管理员" | "教师管理员" | "超管"
 } {
   const roleMap = {
     [USER_TYPE.REGULAR_USER]: {
       type: "default" as const,
       label: "普通" as const,
     },
-    [USER_TYPE.ADMIN]: { type: "info" as const, label: "管理员" as const },
+    [USER_TYPE.STUDENT_ADMIN]: {
+      type: "info" as const,
+      label: "学生管理员" as const,
+    },
+    [USER_TYPE.TEACHER_ADMIN]: {
+      type: "warning" as const,
+      label: "教师管理员" as const,
+    },
     [USER_TYPE.SUPER_ADMIN]: {
       type: "error" as const,
       label: "超管" as const,