Okay, thanks for the clarificatoin.
The bar can be shrunk to a minimum width of the largest required minimum of any element in the side bar. That will either be a component in the action tab or the minimap itself.. The history tab either has no effective min or a min that is always less than any minimap that exists today.
While having it so there is a consistent min across any possible tab would be, consistent, it's not necessarily trivial to do.