> Where does this 3rd party identity token provider come from?

Some oracle whose job it is to print tokens and hand out rolls to the stores (and to the websystems). They would know which store got which roll, and which website authenticated it, but not who each ticket from that roll went to.

With a big enough roll, this is essentially anonymous.

Yes, lotteries know which store got the winning ticket, but they have no idea which of the patrons in the store got it. Not unless they ask Eve to get her telescopic lens and notepad out.