I've been doing API development for over ten years and worked at different companies. Most PMs are not technical and it's the development team's job figure out the technical specifications for APIs we build. If you press the PMs, they will ask the engineering/development manager for the written technical requirements, and if the manager is not technical, they will assign it to the developers/engineers. Technical requirements for an API are really a system design question.
The technical design is definitely the job of the technical team for the most part, but the business requirements should be squarely on the pm. The list of use cases, how the API feels, the performance etc... All of that the business owner should be able to describe to you to ensure it does the job it needs and is fit for the market.
