Good tidings!
To test the purchase flow, I bought one of your works (I like the concept, by the way!). It looks like this site provides valid marketplace listings, in which the act of purchase is a direct lightning payment to you, followed by instructions on how to acquire your piece. I did notice that the site doesn't appear to publish a full zap (kind 9735) event with purchase, which can lead to our mystery buyer scenario.
I think the quickest wins here would be tying the purchase to a zap (perhaps on the marketplace/art listing), as well as adding the option to click a button that sends you a direct message notifying that the user has purchased X art piece.
The current system as designed should work, so long as mystery buyers do the due diligence of reaching out per your instructions. 😅
That all being said, how were you expecting the site to work, ideally speaking?
Also, we've made some advancements in a few of these areas recently in Shakespeare, it might be worth prompting for a new site in the same visual style as this one, with these features requested in the initial prompt.
(CC:
@MAKE SONGS LONGER)