There
is a way to get the Google file picker to show shared files and folders, AND files in shared drives. Note that a shared file and a shared folder is not the same as a shared drive. A shared drive was formerly know as a "team" drive.
What I did was to enable a picker feature
.enableFeature(google.picker.Feature.SUPPORT_DRIVES)
The enableFeature method is part of the Picker Builder class:
var picker = new google.picker.PickerBuilder()
.enableFeature(google.picker.Feature.SUPPORT_DRIVES)
Even though the documentation shows information about:
DocsView.
setEnableSharedDrives(boolean)
The above line produces an error, and doesn't seem to be needed for showing shared files, folders and drives.
I still haven't had confirmation from any users, but it seems to be working for me.