What does this API do? Can I invoke it using my preferred language? What performance characteristics does it have? Is it synchronous or asynchronous?
To that we can add questions about types, latency, protocols, and so on.
But there are plenty of non-technical questions: can I rely on this service to continue operating in the future? Can I be sued for using it, or for using it in certain ways? Can I build a commercial service using the API or the data it provides? If the API provides me with data that is incorrect, or illegal (containing copyrighted material, say), who is liable? What likelihood is there that the people running the service will degrade or shut down the service, demand increased payment for access to it, or offer preferential access to my competitors? Who owns, controls or distributes any data that I share via my invocations of the API? And what happens if or when the answers to any of these questions change, and how can I influence the direction of those changes?
Whether you call these 'political' questions or not is a matter of semantics. I think they're political in the sense that they're about the people running the service, rather than the technology itself. They're about who controls it, who decides the direction of its evolution, and what constraints they operate under. Those questions will depend on business, ethical, regulatory and philosophical considerations, and I don't think it's unreasonable to describe those as being 'political'.