> It is very unclear whether the output of an AI tool is subject to copyright.

At least for those here under the jurisdiction of the US Copyright Office, the answer is rather clear. Copyright only applies to the part of a work that was contributed by a human.

See https://www.copyright.gov/ai/Copyright-and-Artificial-Intell...

For example, on page 3 there (PDF page 11): "In February 2022, the Copyright Office’s Review Board issued a final decision affirming the refusal to register a work claimed to be generated with no human involvement. [...] Since [a guidance on the matter] was issued, the Office has registered hundreds of works that incorporate AI-generated material, with the registration covering the human author’s contribution to the work."

(I'm not saying that to mean "therefore this is how it works everywhere". Indeed, I'm less familiar with my own country's jurisprudence here in Germany, but the US Copyright Office has been on my radar from reading tech news.)