At small sizes, like 8–13px, sans-serifs look better than serifs. And user interfaces and websites used to be that size.
But for 16px and up, which is what websites of today use, serifs are perfectly fine even on 1× displays (though sure, they’ll look better still on higher-DPI displays, but so will sans-serifs).
I should clarify that it depends on the font. Sans-serifs tend to have fairly even stroke width, but serifs tend to have more variable stroke width, and if the thin is too thin, you get a terrible font. That’s a common shortcoming of serif fonts, and Garamond demonstrates that, being quite unsuitable for screen use below 20px, maybe even 24px. Others like Georgia don’t suffer that weakness.
Are you sure that "websites of today" use 16px or larger universally? HN appears to use 9pt Verdana, which I believe is equivalent to 12px on my Windows system if my math is correct.
Georgia is a terribly underrated font. I'm sure it's heavily hinted to look good at small sizes, but even at large sizes it has an elegance that is lacking in e.g. Times Roman.
But for 16px and up, which is what websites of today use, serifs are perfectly fine even on 1× displays (though sure, they’ll look better still on higher-DPI displays, but so will sans-serifs).
I should clarify that it depends on the font. Sans-serifs tend to have fairly even stroke width, but serifs tend to have more variable stroke width, and if the thin is too thin, you get a terrible font. That’s a common shortcoming of serif fonts, and Garamond demonstrates that, being quite unsuitable for screen use below 20px, maybe even 24px. Others like Georgia don’t suffer that weakness.