That's the magic of Apple's leverage. Even though they can't control how websites are built and can't force them to offer sign in with Apple on their websites, with apps adding Sign In With Apple, they must also offer it on their website so that their app users can log in.
A growing list of websites have Sign In With Apple. When you hit Sign In With Apple on a website, if it's on an iPhone or iPad, it'll sign in just like an app. If it's on a Mac, you'll be asked to sign in to your Apple ID on that Mac if you're not already. If you're on Windows or Android, there's a specific code that you can generate to log you in.
Ultimately, Sign In With Apple works best within the Apple ecosystem. If you're a Windows PC and Android household, maybe Sign In With Apple is not the right thing for you.