It’s better to use AuthService for keep the user data. You probably need to make variable for it and change Stream also to that type. And add some function to save and read user data from storage.

GoRouter perfectly works on Flutter web. To keep the login state on browser refresh you should save the state in some persistent storage and get it on app start perhaps you can use splash screen for it. In real-world applications people use may local storage to store access tokens or something to validate the login state.

Sorry for the late reply. I think you can do it using the navigatorBuilder function in the GoRouter. you can get more information from go router documentation. https://gorouter.dev/navigator-builder