You have to tell Github Pages not to generate a Jekyll site, then publish your Hugo output folder into your gh-pages branch. I imagine you can google for some instructions on this. Alternatively, Netlify has a free tier and it’s good alternative.
Github pages was built for Jekyll. You’re swimming upstream using any other generator with it. It doesn’t have https either, unless you use something like Cloudflare. I’ll reiterate my earlier suggestion of using Netlify.