Currently, the US copyright application process has an AI disclosure requirement for the determination of applicability of submitted works for protections under US copyright law.

The copyright office still holds that human authorship is a core tenet of copyrightability, however, whether or not a submission meets the "de minimis" amount of AI-generated material to uphold a copyright claim is still being decided and refined by the courts and at the moment the distinction appears to fall on whether the AI was used "as a tool" or as "an author itself", with the former covered in certain cases and the latter not.

The registration process makes it clear that failure to disclose submissions in large contribution authored by contractor or ai can result in a rejection of copyright claim now or retroactive on discovery.

You do not apply for copyright. In the US you can, optionally, register a copyright. You do not have to, but it can increase how much you get if you go to court.

I do not know whether any other country even has copyright registration.

Your main point that this is something the courts (or new legislation) will decide is, of course, correct. I am inclined to think this is only a problem for people who are vibe coding. The moment a human contributes to the code that bit is definitely covered by copyright, and unless you can clearly separate out human and AI contributed bits saying the AI written bits are not covered is not going to make a practical difference.