They key issue is whether the training is considered to be fair use; but this can only be determined in court. We have some preliminary indications that it definitely can be, but also may not be, depending on four factors, but predominantly the first and fourth factor (how transformative, how it affects the market for the original works).

National Law Review covered some of those nuances last year: https://natlawreview.com/article/federal-courts-issue-first-...

US Copyright Office has a substantial document discussing each of the four factors, and making it clear this is an unanswered question, and details of the particular case will decide which way courts go. It is a prepublication version, and it's over 100 pages, but it covers the issues well, citing arguments on all sides.

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