I mean, IF the API is primarily tailored for UI presentation, there's already a text/html that you can use. I don't see the real problem here. Unless it's a type of API that has multiple purposes. In which case you got to tailor the response/presentation based on the needs.
Either way, the time needed to build a HTML elements will be eventually spent somewhere, on the server or on the client side. Server provides you with the data, you pick the form in which it is sent, and then work around the presentation layer.
I'm helping up the team behind https://voiden.md so I can tell you, it's easy to present the HTML even in the API clients, let alone the website itself.
Either way, the time needed to build a HTML elements will be eventually spent somewhere, on the server or on the client side. Server provides you with the data, you pick the form in which it is sent, and then work around the presentation layer.
I'm helping up the team behind https://voiden.md so I can tell you, it's easy to present the HTML even in the API clients, let alone the website itself.