In the API, you can only access project memberships at the user level. I believe this design decision was made because even in projects that are “comment only”, individual users can be given full access.
I did find a small error in the Project Memberships documentation. If you want to fetch the project memberships record, the docs say to use the project-id:
However, it should actually be the membership-id:
You can get a project’s membership-id with: