CC0 a license that relinquishes copyrights. You’re right that it’s a license and not public domain, but otherwise making a distinction without a difference. The stated explicit intent, and the rights granted by the license, are to provide a version of public domain that is unambiguous and works globally.
Your terminology is a bit funny when you say “I still own the copyright” or “all of these works are copyright”. Works aren’t copyright, works are protected by copyrights that authors have… unless the author waives those rights. The copyright one has by default is the exclusive right to copy and distribute the work. Once you give that away, either via license or public domain attribution, it’s irrevocable and permanent, and there’s nothing of value in the idea that you’re still the copyright holder, since there are no longer any copy rights retained nor copyright protection under any laws.
In short, it’s perfectly fine to call CC0 attributed works “copyright-free” because that’s what the license actually does, it “waives” all copyrights and “related rights”, and allows the public to copy at will, forever.
BTW I don’t think it’s true to say that there’s no such thing as relinquishing copy rights in many countries, that’s too strong of a claim. It is true to say there’s no such thing as public domain, but copy rights (or “related rights”) can be transferred and/or waived pretty much everywhere.