I'm having this issue with Klarna. Which is a total nightmare because it means I can't pay for things which I have purchased, and is majorly stressing me out.
What I found on the apple website, which they really should make more clear is this line:
**If you choose the Hide my Email option, only the app or website you created the account with can use this random email address to communicate with you. **
What that means is that the random email address, in my case, was generated for Etsy, and it was that which was used to set up Klarna, but now when I try to use that same email address to sign in and pay on Klarna, I can't receive a verification code because it wasn't set up specifically for use by them. So nothing they send me to that email address will ever come through.