Example: All data you type in for account registration but do not for purchase.
Easyer tracking directly and indirectly. Data broker use all they can get to identify you, so cross site tracking happens whenever you provide same phone number or mail.
Being able to switch these data points is helpful for privacy. And switching is easyer without accounts.
Answer is simple as always: As much privacy as possible.
So here the question was: Does account creation in this situation affect privacy? It is meaningless, what the threat model is, the answer is always the same.