As the title said, why dont purchases end up in your library?
also, when you purchase a product you have access to it, period. that only works with an account... maybe allow for a checkmark like, itch.io as payment processor only... that might be useful... so people can buy from website without logging in. or making sure people are logged in and creating google auto log in to make it seemless... and yeah... the purchase did not show up... i was kind of exhausted for a couple of days...
There's probably a reason, but I can't know without more information. If you bought a product while logged out, it's connected to your e-mail, and you can recover the purchase using a form on the support page.