If you're looking to retrofit something like this in, just for a simple piece of state like which tab is active, and don't want to refactor all your existing local state management code, Context is a really powerful tool for this.
I think of it like a dedicated state 'portal' - should I need to use one particular piece of local state in other components, I just write a quick dedicated Context for that one piece of data (super quick and simple and React-y using the new API) and simply set the context as well whenever I set that piece of state.
Won't work for everything, is a little hacky in a way and you wouldn't do it that way from scratch, but it's such a quick and easy solution to this issue compared to a major redesign of the global/local state.