Yes. Unless you pay in person with cash, your purchase data will be brokered.

I still want a way to pay with "cash" over the internet, e.g. a prepaid card which I can buy with cash and isn't tied to any person's name or address.

That would be cool for donations too. I often would like to compensate software devs or content creators, but I hate having to create an account and/or share credit card info.

I think someone mentioned "burner" cards a while back.

Privacy.com the App. Let's you do this with burner cards.

Visa and Mastercard have prepaid anonymous debitcards. Then there's cryptocurrencies...

But you still need stuff to be delivered, which means they have your name and address, along with contact information, which can be used to match your purchase history,

If I was Amazon I wouldn't be selling purchase history to Google. Why would I ? I have no need of the money and Google is one of the few entities that present a visible threat to my well being.

Amazon, like every other retail service, has reciprocity agreements with payers (Visa, MasterCard, AMEX, etc.)

Amazon gives up your purchase history to get it from everyone else, for that sweet product retargeting.