I've seen a lot of people use asciinema to record and share terminal recordings, it works quite well

You still end up having to turn it into a GIF if you want it to autoplay on GitHub's markdown viewer, or video if you want it to run on the page but require a click-to-play.

Huh, I though you could embed those into READMEs on GitHub, but turns out you can't

How would that solve the font problem? I feel like that would only make the problem of having unsupported fonts even worse.

One solution could be to use the docker version of vhs, and edit the dockerfile to pull your desired font.