feat: Add invite code field to registration form

Frontend Changes:
- Added inviteCode field to registration schema (optional)
- Added invite code TextField to registration form UI
- Updated RegisterData interface in AuthContext to include inviteCode
- Pass inviteCode to backend during registration
- Added helpful placeholder text indicating field is optional

User Experience:
- Invite code field appears after email in registration form
- Helper text explains it's optional and can be left blank if registration is open
- Backend will validate the code if REGISTRATION_MODE=invite_only

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

maternal-web/lib/auth/AuthContext.tsx

@@ -31,6 +31,7 @@ export interface RegisterData {
   password: string;
   name: string;
   role?: string;
+  inviteCode?: string; // Required if REGISTRATION_MODE=invite_only
   dateOfBirth: string; // COPPA compliance - required
   parentalEmail?: string; // For users 13-17
   coppaConsentGiven?: boolean; // For users 13-17
@@ -240,6 +241,11 @@ export const AuthProvider = ({ children }: { children: ReactNode }) => {
         deviceInfo,
       };
 
+      // Add optional invite code if provided
+      if (data.inviteCode) {
+        payload.inviteCode = data.inviteCode;
+      }
+
       // Add optional COPPA fields if provided
       if (data.parentalEmail) {
         payload.parentalEmail = data.parentalEmail;