Style not loaded in new window

I reproduced the problem with minimal code on this Stackblitz .

I made part of my component open on a new window BUT it should still be able to interact with my main app. I used DomPortalHost to achieve that. The interaction works successfully but the style are not loaded into the new window.

How do I force the new window to match the style of the main app?

The main app

The window:

from Style not loaded in new window