As mentioned elsewhere, I use Hexo as my static site framework. It does most of what I want out of the box, and it has plugins for most everything else.
On my homepage I’ve embedded the SoundCloud widget in a Bootstrap flexbox. But it would be nice to put audio directly into a blog post as well, without too much hacking. Fortunately, Hexo has plenty of audio plugins available, and in less time than it took to write this post I added a couple.