Generally, it should work out of the box. The only note – if you are trying to show the codes on Shop pages – please make sure that main variable product (i.e. not variation) has EAN set.
If that doesn’t help – would it be possible to share access to your site, so I could log in and check what’s going on (my email is [email protected])? Please let me know if sharing an account is not an option, and I will continue solving it remotely.