I think that what we buy online is already monitored and the data sold. Buying online with a credit card sort of is already giving up privacy in a big way, so I don’t think that earning crypto on top of that is giving up anything additional. While transferring to a wallet of course then is traceable and attached to your name, so is buying from most exchanges. I do use a separate wallet for the BTC I’ve earned though, just because I use a few to keep things separate etc.
I would say for those that are more worried about privacy then something like fold app could be good. You can buy gift cards anon and earn btc off that.. it’s just not as user friendly.
They do not store the data though, from my understanding.