Hello,
i have exactly this same problem on ASUS ZENPAD8.
My application calls picker and no SDcard to pick.
SDcard is ok, because if I want to see files on SDcard using system File Explorer - SDcard is working, files and folders are displayed.
Calls in application probably are ok too, because my application works fine in Android Studio emulator with emulated SDcard.
I think, my problem is in tablet settings, but I don't know where.
Please explain to me how you solved it - I didn't understand it from the Helen description in the thread.