If you're calling APIs that you have no control over, you do so on your server.
That's the entire point of HTMX: the minimal necessary addition to browsers/HTML to allow HTML REST APIs to update pages without full page loads.
Obviously you _could_, and it might even work well, but I think that's using the tool against its grain.
Htmx is "bring your own backend", but you do have to have a backend, be it Haskell or Zig or Gleam, that talks to your API, and renders HTML.