Re: Barking up the wrong tree
"But what if the two sites KNOW each other."
That would not matter. E.g., the Facebook cookie in the Register session would be different from the Facebook cookie in the Amazon session, and both would be different from the Facebook cookie in the Facebook session, meaning that Facebook would not be able to slurp the articles that I looked at.
So that would work unless they shared identities (i.e., your account information).
As for "Isn't that why you have multiple browsers installed?" Yes. I have Firefox, Opera, Edge, Chrome and Vivaldi. I am running out of browsers.