To help you keep your personal information more private, Apple offers an option for users to hide their email addresses. Hide My Email service basically creates unique and new email addresses that act as your own without revealing your true address.
What it does is forward all your emails to your inbox even if you are appearing as a random email address on different websites. You can only do so if schuh website or app supports the Sign in with Apple option.
However, many users complained that the Apple mail feature does not forward any of their messages to Gmail or any other email client. Their real email address does not receive them.
Fixes for Hide My Email Apple Service Not Receiving or Forwarding Any Emails Issue

It is bothersome not to receive any of your emails. Some important messages may have already been missed. So, let’s take a look at what we can do to deal with this problem.
First, verify if you have the correct email address. There might be a wrong letter or character. If everything is perfect, check the Spam folder in case the message was sent there.
You can try to deactivate and reactivate your email address on Hide My Email. Launch icloud.com/icloudplus and login to your Apple account. Select Hide My Email. Choose the problematic email address and select Deactivate email address. Continue with the process until you deactivate it.
Now, you need to reactivate it by following the same steps as above. This time, look for the email address and select Reactivate address. Continue with the process until done.
Another way is to make sure that your iCloud subscription is fully activated. You may need to verify the status since Hide My Email feature can only work if your subscription is fully active.
If you still continue to experience the error, you can seek assistance from Apple Support. Head over to this page, getsupport.apple.com, and talk to a customer support.
In Summary
There are several methods that you can do to try and resolve the issue with Hide My Emails. Best of luck and hopefully, the problem gets solved soon.