It doesn't work on iOS 16.2 for sure.
I logged in with Sandbox user in AppStore settings, verified email, phone (before tried without it but had same result) but trying to make a purchase in the app it shows my primary Apple ID account and requests the password exactly for that account.
Interesting, that I made it work ONLY if I used Sandbox account as a primary Apple ID - I logged out from my Apple ID and logged in with sandbox user id. That was a pain, as you understand, but only that works