Google was already in the middle of a class-action lawsuit regarding the incognito mode, where they were accused of tracking user activity. And, they agreed to settle the lawsuit.
To conclude that and move on, they will have to make the necessary changes to prevent another lawsuit against them.
Firefox’s private mode says:
https://support.mozilla.org/en-US/kb/common-myths-about-private-browsing
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Ok. I’ll leave it just in case someone else doesn’t.