To address the issue in the title, the “correct” option would be for us to use zh-Hans and zh-Hant, but the browsers are inconsistent with the options they present.
Chrome:
Firefox:
I can’t find any way in Safari to pick a language, so it must always use the system settings? That potentially includes all these options:
Documentation suggests a language code like zh-Hans_HK is possible from macOS. I do wonder if that makes it to the browser.