I noticed, that when I open the link Public websites (in German Öffentliche Website) from the left navigation menu, a new tab is opened in the browser. This is the only link in the top section of the navigation bar, which does that. This is a little bit unexpected from a users' perspective, I think.
My suggestion would be to have the page displayed inside the Admin Center or, if it's not possible, mark the menu entry with a symbol/icon.
@Mourad Louha - A lot of updates and features have been checked into the new Admin centre since this was raised. I am having problems repro this - can you confirm if this experienced has improved to what you raised ?
the menue entry Öffentliche Website for the public websites shown in the screenshot of my first post here has been removed from my Admin Center. I think, that's because of public websites have been discontinued, if I am well informed. So, it's not possible to repro and the problem I described in my post above has gone. Independently from that, thanks :)