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/types.ts

@@ -33,7 +33,7 @@ export interface Profile {
   submission_number: number
 }
 
-export type UserAdminType = "Regular User" | "Admin" | "Super Admin"
+export type UserAdminType = "Regular User" | "Student Admin" | "Teacher Admin" | "Super Admin"
 
 export interface User {
   id: number