feat: AI quiz generation per lesson + hide edit buttons for non-authors

- Generate unique quiz for each lesson using OpenRouter API
- Parse lesson content (TipTap JSON) and send to AI for question generation
- Cache quiz in database to avoid regeneration
- Hide Edit/Delete buttons if current user is not course author
- Add backendUser to auth context for proper authorization checks
- Show certificate button prominently when course is completed

Co-authored-by: Cursor <cursoragent@cursor.com>

apps/web/src/contexts/auth-context.tsx

@@ -6,8 +6,17 @@ import { getSupabase } from '@/lib/supabase';
 import { useRouter } from 'next/navigation';
 import { api, setApiToken } from '@/lib/api';
 
+interface BackendUser {
+  id: string;
+  email: string;
+  name: string | null;
+  avatarUrl: string | null;
+  subscriptionTier: string;
+}
+
 interface AuthContextType {
   user: User | null;
+  backendUser: BackendUser | null;
   session: Session | null;
   loading: boolean;
   signUp: (email: string, password: string, name: string) => Promise<{ error: Error | null }>;
@@ -20,6 +29,7 @@ const AuthContext = createContext<AuthContextType | undefined>(undefined);
 
 export function AuthProvider({ children }: { children: React.ReactNode }) {
   const [user, setUser] = useState<User | null>(null);
+  const [backendUser, setBackendUser] = useState<BackendUser | null>(null);
   const [session, setSession] = useState<Session | null>(null);
   const [loading, setLoading] = useState(true);
   const router = useRouter();
@@ -64,8 +74,9 @@ export function AuthProvider({ children }: { children: React.ReactNode }) {
     const tryExchange = () => {
       api
         .exchangeToken(session.access_token)
-        .then(({ accessToken }) => {
+        .then(({ accessToken, user: backendUserData }) => {
           setApiToken(accessToken);
+          setBackendUser(backendUserData);
           setLoading(false);
         })
         .catch(() => {
@@ -152,6 +163,7 @@ export function AuthProvider({ children }: { children: React.ReactNode }) {
     <AuthContext.Provider
       value={{
         user,
+        backendUser,
         session,
         loading,
         signUp,