If you have a style selected for navigation it is lost when you are in the menu item.

I would argue the menu item should still be styled.
I don't know why it has that gray border either.
Yes, that was super confusing. I guessed it was a 'nothing' state but had to think about it a bit. I was going to create an issue about that so will do, because it's on all once you click in.
Yes, I will remove the border and see how to preserve the style in edit mode.
Related to this I get the following where the theme styling seems to vanish:

Please try to get this one before to start to work on this.
It seems it was tested with an old master version since now the background color is applied to the whole navigation menu.