SP members not able to move files

I'm seeing the same issue now after I created custom permissions, Contribute but with Delete item and Delete Version not checked. I wonder if it's the no delete option, since moving a file in SharePoint is basically deleting a file then recreating it in the new location. It's the same reason you'll get a High Volume Deletion email alert when you move a lot of files at once to a new location.
I'm not sure why the error would say it's about content approval, but after much testing, I only get that error when delete is unchecked.