Earlier quoted context omitted.
> RESTful APIs serving up JSON works for all 3, as does GraphQL (not a fan, but many are). This however is totally web-specific HTML is a machine-readable format, like XML and JSON. Have your back end represent a given resource as microformatted-semantic markup, send it gzipped over the wire, and you've got the data exchange you need, even if your mobile app isn't already dressed-up webview.
Are you still referring to dedicated API routes, or are you talking about annotating your UI to the point where it can serve as the API as well? I remember the latter being the vision behind things like RDFa, but those approaches never took off, for a variety of reasons.
At that point you might as well serve XML and use an XSLT transform (+ CSS) to render the view on the client (yes, this is still possible without JavaScript).