“Limited access” is an older iOS feature from 2020, and different from the “private access” photo picker introduced with iOS 17[1].

[1] https://developer.apple.com/videos/play/wwdc2023/10053/?time...

Limited access isn’t great UX because it’s not reasonable for users to have to manage a list of photos for every app. The new one is much better, but unfortunately app devs have to opt into it for now.