Might be too late now, but this worked for me: https://gist.github.com/JadenGeller/afb907745865052ed59c53b5ca9f8671
Update: I've just notice this Xcode debug warning when running the app:
Presenting view controller <PHPickerViewController: 0x103240080> from detached view controller <UIViewController: 0x1036bcca0> is not supported, and may result in incorrect safe area insets and a corrupt root presentation. Make sure <UIViewController: 0x1036bcca0> is in the view controller hierarchy before presenting from it. Will become a hard exception in a future release.
So it might not be a viable solution
Cheers
Gavin
gjerman
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On the page you link to with the video, there is a Resources section with a link to "Building a document-based app using SwiftData". This page has a download for the sample project code - https://developer.apple.com/documentation/SwiftUI/Building-a-document-based-app-using-SwiftData.
Gavin