If we agree that a RESTful API should offer more or less the same functionality as the UI, then we can use the same tests for UI automation and for API testing, provided that we make the right abstractions and link them together properly -- this will guarantee that the API is navigable and respects the HATEOAS principle.
HATEOAS, for those wondering, stands for Hypermedia As The Engine Of Application State, which is a fancy way of saying the REST application exposes its state (where resources are and how you can interact with them) via hypermedia embedded in API responses. The advantage of this is:
A REST client needs no prior knowledge about how to interact with an application or server beyond a generic understanding of hypermedia.
In practice, HATEOAS is often left off (which pretty much defeats the purpose of REST, but c'est la vie). The result is a "RESTful" API. Meaning it's like REST but it ain't really REST. I like well-designed RESTful APIs because they are easy to navigate logically, but true REST APIs don't need to be navigated at all, which is way cooler.
But I digress, back to Mihai and this excellent post on testing:
The code that tests the UI should also test the API. It is achievable, provided that the architect pays as much attention on the tests as he does on the app’s code (which, sadly, is not always the case).
He goes on to show example code testing the GitHub API. Good stuff 👌