My last comment was wrong, I've read through the filings of the case.

The judge has already ruled that training the LLMs using the books was so obviously fair use that it was dismissed in summary judgement (my bolds):

To summarize the analysis that now follows, the use of the books at issue to train Claude and its precursors was exceedingly transformative and was a fair use under Section 107 of the Copyright Act. The digitization of the books purchased in print form by Anthropic was also a fair use, but not for the same reason as applies to the training copies. Instead, it was a fair use because all Anthropic did was replace the print copies it had purchased for its central library with more convenient, space-saving, and searchable digital copies without adding new copies, creating new works, or redistributing existing copies. However, Anthropic had no entitlement to use pirated copies for its central library, and creating a permanent, general-purpose library was not itself a fair use excusing Anthropic's piracy.

The only issue remaining in this case is that they downloaded copyrighted material with bittorrent, the kind of lawsuits that have been going on since napster. They'll probably be required to pay for all 196,640 books that they priated and some other damages.