AI bots never had rights to waive. Their work is not their work.

This is only partially true. In the US (which tends to set the tone on copyright, but other jurisdictions will weigh in over time) generative AI cannot be considered an "author." That doesn't mean that other forms of rights don't apply to AI generated works (for example, AI generated works may be treated as trade secrets and probably will be accepted for trademark purposes).

Also, all of the usual transformations which can take work from the public domain and result in a new copyrightable derivative also apply.

This is a much more complex issue than just, "AI bots never had rights to waive."

Public domain absolutely exists in the EU.

Hmm. There was some kind of issue with that in the EU that led to the creation of a Creative Commons license, IIRC. Maybe nonstandardized handling of stuff not under copyright. I remember that in the US, putting something in the public domain wasn't an issue, but in at least some of the EU, it was important to use Creative Commons instead.

I think that something not being under copyright isn't analogous everywhere.

googles

https://en.wikipedia.org/wiki/Public-domain-equivalent_license

In 2009, Creative Commons released CC0, which was created for compatibility with jurisdictions where dedicating to public domain is problematic, such as continental Europe.[citation needed] This is achieved by a public-domain waiver statement and a fall-back all-permissive license, for cases where the waiver is not valid.

In some countries, that might be the case. However, in Germany (where I live), there is no way to have something "not copyrighted". The author holds the copyright unless explicitly licensed. (Here's where the CC0 comes in handy, but the CC licenses weren't made for software...)