And I expectected that using author="$current" will show only the parent post assigned to current logged in user. But it does not work. What can be wrong?
I have also tried to switch theme to Twenty Nineteen and deactivate all other plugins.
I have feedback from the developers that the use_select2 attribute is intended only for use with older Types 2 relationships and should not be used with Types 3 relationships.
They state that because of how this is implemented it is not possible to make attributes such as author work when also using the use_select2="never" attribute, and if any changes were to be made it would be to ignore the use_select2 attribute on anything except old Types 2 relationships.
So, I'm sorry, it won't be possible, and it is clear from the response of the developers that if a feature request were made to support this it would be rejected.