Here are two ways to pay for things without the payment method being a direct line to you:

Use cash. People will say stupid things like “I’m European and live in a surveillance state and they track the serial numbers!” Let me introduce you to something called “money laundering”. What you do is ask for change or for a big bill. You may need to be a normal person, like a customer of some sort, or a non schizophrenic shut in computer nerd if asking of some person (like a bartender getting off at shift change!).

Use a gift card. People will say stupid things like “well, they know you bought a gift card, so they can tie it back to you!” Again, allow me to introduce you to the vagaries of something called money laundering. Have someone else buy and activate the gift card. Heck, if you really want to be a weirdo about it, do it with your friends and put all your other person purchased gift cards in a fishbowl and draw random ones out.

Gift card stuff is something to poke and prod at first because different stores and cards have different ways of adhering to kyc.