With the latest 2025 October you may achieve this scenario using Login widget
1. In the Experience Builder app Add a Login widget
2. at privacy & security enable both "Skip sign-in prompt for secured resources" and "Skip credential banner" so that anonymous users won't see login prompt for the non-shared feature layer

3. share the app publicly
4. Anonymous user can view the app without loading the non-access feature layer
4. Organization user can login through Login widget and the app will load the feature layer if they have access