I would suggest "Anthropic client", because the relationship between them and Anthropic is similar to the relationship between a client and a contractor.
You ask the contractor for what you want, iterate a little, and take what they give you. Sometimes you may read the results.
Nobody calls the person that manages a company’s external contracts a client internally though, we call them something like “contract manager” or “acquisitions specialist” if the contract is with a manufacturer.
You ask the contractor for what you want, iterate a little, and take what they give you. Sometimes you may read the results.