macOS doesn’t really. There’s App Store, with varying degrees of success. And then most other apps use Sparkles framework, a third party library.
I am surprised that something like sparkle hasn’t found footing on Windows.
re. Sparkle - same. Sparkle is practically the platonic ideal of a self-update framework; there's good reason why it's been the uncontested standard on the platform for nearly twenty years (!!).
As a user, I hate Sparkle. At least, I hate Sparkle's default mode where you have to click "Install Update", then wait for the update to download, then authenticate, then wait for the update to extract, then wait for the app to relaunch. Too slow. When I open an app, I want to use it, immediately. I'd rather have apps update in the background; barring that, at least give me a button to manually start a background update while I continue to use the older version of the app.
Sparkle does have that for a long time now, but the default does still want you to agree to background updates the first time. Developers can turn that off and make apps update silently in the background (when they're running).