GP's (or rather GGGP's) statement was "I did not write that code but I paid money". So they claim no authorship. Anthropic is a company, they can't be the author either. So the only one left as author in that reasoning is Claude.

I don't think that necessarily anthropomorphizes it. We speak of monkeys as authors without calling them human. And really the legally important fact is that there was no human author. You can also treat it like CCTV footage which is generally not under copyright because there is no human author (even though most would hesitate to call the camera the author either)