The only workaround that seemed to solve it in my situation was quite simple: Changing the presentation mode from .automatic (which is .pageSheet on iOS >=13 in my understanding) to .fullScreen (the previous default). Might not be 100% the desired UX for everyone, but after some hours of trial and error I found it quite close enough. I suppose the pure SwiftUI equivalent would be to use .fullScreenCover (iOS >=14) instead of .sheet, but I didn't try that, as I'm presenting a UIDocumentPickerViewController programmatically for unrelated reasons.