You do not need to request any sort of OS permission or Drive API access to read or write Drive files that are selected using the system document picker. You do need to specify that you want a writable file when you open the picker. The system will grant your app write permission for that file URI only.
> So then the app can't have Recent Files functionality.
Yeah, this is an issue. Google really needs to fix this. And there are multiple ways to do that! They can remember that a file was opened by the app earlier, and let it access again for a reasonable period.
They can also allow delegating access on a directory level instead of a binary all-or-nothing approach.
Android DOES remember permissions for folders that you have opened previously through the picker (although the app does have to code for that); and you can reuse the URLs for files that you have received through the picker, as long as the permissions are still intact. (You can lose them if the app is used infrequently).
Life would be so much easier if the Android File Picker UI weren't so incredibly awful. Has to be the worst piece of UI design I have ever seen. Incredibly difficult to use even if you know exactly what you want.