Anthropic now provide Indemnification as well:

Our Commercial Terms of Service (previously our services agreement) will enable our customers to retain ownership rights over any outputs they generate through their use of our services and protect them from copyright infringement claims. Under the updated terms, we will defend our customers from any copyright infringement claim made against them for their authorized use of our services or their outputs, and we will pay for any approved settlements or judgments that result. These new terms will be live on January 1, 2024 for Claude API customers and shortly after for those using Claude through Amazon Bedrock.

Anthropic on LinkedIn:

We’re introducing new, simplified Commercial Terms of Service for our customers with an expanded copyright indemnity, plus an improved developer experience…