Vlad You know, I never noticed it doesn't say "private." I look for color cues. Here is what a new tab page looks like for me.
And this is what a private tab looks like for me
Very slight color difference at the top. Also "search or enter website name appears twice. I've seen this before. Figured it was just a minor bug, not worth reporting, but seems it only appears in private mode, not non-private. I can't remember if that was always the case.
Also, if window is not maximized, the words run over each other, like this