GDPR is not copyright, despite all similarities. I assume that you accept that copyright does not work like that, since you are changing the subject.
Note that the GDPR does not claim to be applicable in third countries; ie outside the territory where EU law is enforced. It only seeks to regulate dealings of outside parties with people in the EU. Even that can't be practically enforced, usually. Once data leaves the EU, there isn't much EU governments can do about it, which is why the GDPR has serious rules about data transfers to third countries. (That's a problem for the fediverse.)
You can read the IA's take on these issues here: https://blog.archive.org/2023/11/02/internet-archive-submits-comments-on-copyright-and-artificial-intelligence/
Their take is quite different from the sentiment that seems to prevail in this community.