That is not the reason for the lawsuit. What the lawsuit claims is that Google is collecting information from users when they are using Chrome incognito mode.
I don't think a new incognito tab warns you about that.
Google does not collect any information through Chrome though in incognito mode. Google can see your activity if you visit Google in an incognito window, but any web site can.
How can Google stop collecting user information on the incognito mode if it doesn't know if the user is using it? Do you want Chrome to explicitly advertise user's usage of the incognito mode? Even beside of the incognito mode issue is it even technically possible to serve users without collecting their information? There are bunch of regulations based on user's geographic information and at least you need to collect their IP address. Or are you suggesting that IP address is not a user information?
An incognito mode explicitly informs that "Your activity might be visible to website you visit". Unless you are intentionally trying to conflate Google and Chrome as a single entity, it's pretty clear that Google is going to collect some degree of user information. Let's stop being ridiculous here.
The only thing that's unclear to me, is whether Google is doing this through Chrome (despite Incognito mode), or whether they're doing it via the websites users visit (e.g. via Google Analytics embedded there). The former would be a lot more damning, but it kinda of sounds like it's the latter that they're being sued for? (See also https://www.bloomberg.com/news/articles/2022-10-11/google-s-....)
Journalism really is pretty dead these days - tell us something we don’t know