For me, this is a bug of the OS or the browser. On my OS, Noto Sans is the default sans-serif font and Noto Mono the default monospace font and they pair impeccably. Whatever font you are telling my browser to use will probably be worse for me (at least because of the loading time, and because it is actually hard to match the readability of Noto in my opinion).

It's unfortunate Courier New is both so badly different from the regular fonts (and so bad at all, by the way) and also the default on Windows.