What kind of system would you propose (or do you envision) for applying visual styling to HTML markup in modern web pages today?

You can keep it high level but your comment makes me think you have something in mind, and I'm honestly curious.

I am not sure what a purpose-built tool would look like, but the CSS-like language you see in UI frameworks like GTK is tailored for styling actual UI's.

In CSS on the web, just centering a div has historically been a problem. We have flexbox now, but what if CSS was designed with our current needs from the get-go?