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.

My (limited) understanding was that without formal registration you cannot file any infringement suits against any works protected by said copyright. Then what's the point of the copyright other than getting to use that fancy 'c' superscript?