How can I prove that I have ownership over code I wrote myself, and that it isn’t copyrighted somewhere in the world? How can anyone prove that code is written by a human or AI (if you don’t commit obvious AI harness files and folders)?

Developers also “generate” code and are also “trained” on code they written as freelancers or employees for others which is potentially copyrighted. In that aspect just because it’s written by hand, doesn’t imply the writer has copyright on it.