The main target of the Godot Engine are game developers. But Godot's easy workflow and functional UI elements, makes it also a good fit for non-game applications. There are already some out there you may know, like Pixelorama, an Open Source 2D sprite editor.
You could pretty easily do this as an autoload so it's accessible from anywhere. You could store the actual state as a dictionary or a resource, or even a whole db if you wanted depending on what you're storing.
It's a little old but looks like someone even implemented a redux inspired store! https://github.com/glumpyfish/godot_redux
No idea if that still works, but probably would be too hard to use it as inspiration or even update it to the latest 3.x version