The problem is that the API layer of the browser is now so complex that even without cookies, just your config yields a completely unique signature whether or not you're in incognito.
Basically unless you use a completely different computer for incognito browsing, any site you visit can link your logged-in identity to your browser fingerprint and then track you regardless of mode/cookies.
I was "unique" on two different session tabs, and also in a Private window; reloads, however, were stable. That means that the browser is not recognizable, just the session.
I didn't, but if it's trivial to ignore those fields, then why isn't the proof of concept doing that? I think because you don't know, in advance, which fields to ignore. Demonstrating tracking like that is the point of the page, and it failed to do so, so my conclusion is that it's not that straightforward after all.
This site gives you the details: https://amiunique.org/fp
Basically unless you use a completely different computer for incognito browsing, any site you visit can link your logged-in identity to your browser fingerprint and then track you regardless of mode/cookies.