It's a shame that on VS Code at least (I'm not sure if this applies in other contexts), the "textual healing" feature goes hand-in-hand with ligatures. There is no way to enable textual healing if you prefer not to use programming ligatures.
There are even checkboxes on the page to simultaneously disable ligatures and enable texture healing. They're just controlling whether various subfeatures of font-feature-settings are off/on.
I have a bunch of font-feature-settings subfeatures turned off explicitly in my userChrome.css, so it took me a little while to realize that that was what was messing with this site. I couldn't figure out what texture healing was supposed to do because toggling it wasn't helping, but it was because of my userChrome.