How do I integrate with extension background?

[cani1see]

I'm trying to use Redux in an extension. The extension environment has separated parts.
I set up Redux in the background and use webext-redux to sync with the UI. That's the solution I use to address the different parts.

redux-devtools seems to rely on the Redux store being in the UI, which is not true in my case. How do I set up redux-devtools in this situation? It could be a new window or a tab in the Chrome dev view.

here is a showcase project