Anthropic gets a lot of it's business via AWS Bedrock so it's fair to say that Amazon probably has reasonable insight into how the Claude usage is growing that makes them confident in this investment
They are also confident in the investment because they know that all the money is going to come right back to them in the short term (via AWS spending) whether or not Anthropic actually survives in the long term.
Nope they have supported AWS deployments for a long time, and now even more of the spend will be on AWS.
> Anthropic has raised an additional $4 billion from Amazon, and has agreed to train its flagship generative AI models primarily on Amazon Web Services (AWS), Amazon’s cloud computing division.