The problem has been solved!
With a new setup, file sharing via link was possible. After restoring the old data and config files, it was blocked again.
Background: I’m using team folders and there is one group, where all users are included. And this group didn’t have the permission to share via link… 
Solution: I created a new group “no filesharing” and blocked this group for sharing. I added all the users to this group, which shall not be able to share via link.
I apologize for causing such a mess. Thanks for your help and have a happy new year!