Earlier quoted context omitted.
Which API reveals my system fonts to a website? Edit: The fingerprint test at https://panopticlick.eff.org/ shows my System Fonts
I don't think you can enumerate them these days, but you can test for them by trying to use them in CSS (which font is used would affect the width of a span of text, use a wildly different fallback font and you can guess which is installed) or (where you can inspect the actual pixels rendered).
@font-face {
font-family: "Roboto";
src: local("Roboto"), url("https://example.com/user-does-not-have-roboto") format("woff2");
}