It looks like some kind of interface between Chrome and the macOS font system has changed on Catalina.
We ran some tests here, and saw the same behavior and rendering. There’s a long list of fonts we suggest in our CSS, with Hiragino Kaku Gothic Pro getting first position. Further down the list are fonts that are on Windows, or fonts we recommend to our Linux users.
Chrome is no longer matching against the font family name “Hiragino Kaku Gothic Pro”, instead falling way down to a chunkier alternative “Osaka”. But! It does match against the PostScript font name "HiraKakuPro-W6”.
There are problems with specifying the font with the PostScript name, though. First, it’ll mess up the browsers that are working well. Also, that’s a font name, not a font family name, so it includes the weight. If we put the PostScript name in the list, it’s going to make a bunch of other stuff look weird.
I logged a bug with Chrome (submitting it into whatever black box the “report a problem” window represents). We’ll keep an eye on this, but I’d say use Safari for a while, and watch out for a Chrome update. Maybe they’ll fix it in the next release. Safari has the benefit of being way better for battery life if you’re on a laptop, too.