You could keep the source files in GitHub and use their web editor to add or update content, then build and push to the publishing server via a GitHub action.
You can find descriptions of such a setup by googling.
> then build and push to the publishing server via a GitHub action
I have looked into this before, but it honestly just seemed very esoteric and complex. I'm surprised that Github doesn't provide pre-made "recipes" for this stuff.
You can find descriptions of such a setup by googling.