Performing a Design Copy on an object does not
link the referenced objects to the Project.
This appears to be a limitation in the Design Copy function.
Please see Dassault BR Article #: BR10000008511
In order to work around this a custom script could be developed
that will attach the related objects to the Project.
Or
you can use Project Based Authorizations. If you perform a Design Copy on
a structure that is Linked and Secured to a Project then the related objects
for the new structure will be Linked and Secured to the Project.