The idea of HATEOS is that HTML isn't "presentation logic", it IS the state of your application. Then, the backend manages the state of your application.
Yup. Another way to frame it is a "return to form" by moving app and business logic back to the server. Technology like HTMX and Datastar are optimizations that allow for surgical updates of portions of the client DOM, instead of forcing full-page refreshes like we did 25 years ago.