Only if the shop assistant took your ID, photocopied it and stored it in a box marked “do not touch” under the counter, alongside transcriptions of everything you ever say inside the store.

Hmm no, because in the case of purchasing alcohol the ID check is 1:1, in time and in space, it's ephemeral (unless the clerk has extreme photographic memory).

In the case of an online-based ID check, even with nice looking privacy terms, there is no guarantee that your ID won't be stored forever and/or re-analyzed many times cross-checking with other services, and worse leaked.