IMO it will be very difficult to shield yourself from a dedicated team trying to track your purchases. Even if you buy on robosats or bisq, they can correlate timing and amount of bank transactions... but this is high effort

So to me the question is whether my identity can be revealed in an easy database pull, because I don't think anyone will be interested enough in me to actually try to link across datasets.

Thus, buying with credit card is KYC. Your credit card company has your identity. Feds ask them to dump all customers that bought from the exchange. Boom, you're on the list.

Buying gift cards is likely a bit more secure. Feds would have to get a list of gift cards used from the exchange, then they will have to correlate those gift cards to users via Amazon (so they would need cooperation of two entities, not one, and at least two database pulls and a merge)

Even more secure, don't use the gift card in an online account linked to your identity, but use the gift card to buy anonymously at a store.

Of course, maybe I am too optimistic and the feds already have backdoors at the exchanges and at the vendors, in which case GG.