Right, like the browser/app environment would be responsible for it, and then devs can hook into that if they want to handle it or not?

To be clear, the operating system is responsible for keeping track of timezone changes. Every major OS has a way for applications to be notified when the timezone changes. The major browsers are already hooked into these notifications, so what I'm suggesting is that when that event is received by the browser they should also emit a "timezonechange" event on the window. Any further handling is up to the developer.