anthropic was _not_ sued for including data scraped from public websites. they were sued for including data extracted from pirated books.
IIUC that was for illegally downloading ebooks and other media -- it had nothing to do with training per se. Scraping publicly accessible data is generally legal, although Microsoft/LinkedIn clearly think they have enough of a leg to stand on to at least litigate this.
Not an expert but there was a court ruling in the US I think last year where circumventing login protection through bot operated accounts when the login is intended for human use was ruled as violation of CFAA. The current state of litigation in the US seems to be that scraping public facing data/websites has been considered as permissible by the courts but data behind a login intended for humans is not. I think there's still a split between the circuits, so this will go through some years of appeal yet.