I’m not sure about the interest, but for those interested, I made a Docker image, which acts as a glue between GitHub and Netlify.
Whenever I push site changes to the private repository on GitHub, the selfhosted GitHub Runner will trigger and pull the changes, build the site and publish on Netlify.
It is based on OpenSUSE Tumbleweed. Because of that, I’ve decided against publishing the image on Docker Hub. The most recent is the one you build yourself.
It’s not perfect, but it works.