It seems like the wrong tool for the job to me, but I was curious and thought about it a little:

After initial page load, a service worker could intercept all the HTMX app's AJAX requests, but it could only work with what's already cached. Using a lot of tooling like workbox the developer could pre-cache the entire app. (Would that mean no dynamic responses?)

Alternatively, implement the entire HTMX app in JS, build the app once for the NodeJS/Deno backend and once for the front-end. After page load, the frontend could take over.

Or something like that. It's a bit convoluted as PWA solutions often are.