Further playing around with the New Window tells me that I can use the View>Tools>Layout> Save and Restore functionalities to manually bring the project settings into the New Window. Not very satisfactory, please have the New Window functionality save an anonymous temporary copy and the initiated window restore it.

Special observation: there seems to be a path where the new window does not get to see the list of saved Layouts, it showed up empty. Took me by surprise so I don't have further details.