When you click the browser back button as far as I remember Remix will do what the browsers do and show the previous data, but if you click a button in the UI to navigate to the previous page it will fetch the new data.
Re global state, in my experience with Remix and before it with tools like React Query, once you move the server state (data fetched from an API or queried from a DB) outside tools like Redux, then what you have left is mostly UI state (input values, open/close states, etc.) and you don't need Redux for that.
And if your app is more complex (like a canvas-like app for example) you can either use a state + context in a parent component or you can use Redux or any other state management library, Remix once JS load will not cause a full page navigation so if you initialize a global state in something like Remix it will keep working across page navigations, even if you click back it will keep the state because Remix uses RR to navigate so it's pure client-side navigation.