Logging into google account on firefox - negates privacy benefits or not?

Hello,

I am in the situation that probably a lot of people are - I have lots of functionality for using the internet tied through google services and my google account - passwords, payments through gpay, email, youtube, google drive, and so I would like to keep the benefit of having these features without sacrificing my privacy.

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If I switch to firefox and also log into my google account using that browser, does it negate the privacy benefit of …

account benefits firefox google google account logging privacy