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/constants.ts

@@ -133,7 +133,8 @@ export const CONTEST_TYPE = {
 
 export const USER_TYPE = {
   REGULAR_USER: "Regular User",
-  ADMIN: "Admin",
+  STUDENT_ADMIN: "Student Admin",
+  TEACHER_ADMIN: "Teacher Admin",
   SUPER_ADMIN: "Super Admin",
 }