The 9th Circuit Court of appeals recently published this that is somewhat related (Amazon v. Perplexity): https://cases.justia.com/federal/appellate-courts/ca9/26-144...

Look at pages 10-17 to see how the law is evolving here.

In Perplexity's case everything is getting routed through the user's browser, so there is no server to server communication between Perplexity and Amazon, thus no CFAA unauthorized access was established. However, Anthropic and OpenAI did not use the pattern of routing through authorized parties, so I don't think this opinion gives them any cover.