Restoring from iCloud after the Apple ID changed

Hi Experts

A while ago I switched to another ISP and I had to switch e-mail address as I could no longer use the old address from my old ISP. Due to that I also had to change the e-mail address used for my Apple ID. I followed the instructions in the support article requesting you to sign out of all Apple devices before changing the address.

Today I accidentally deleted some photos from my iPhone as I was transferring other photos to my Mac. I thought it was no problem since I am using iCloud backup on my iPhone and it had just made a backup. However when restoring the backup I am prompted for the password for my old Apple ID (my old e-mail address) in order to restore purchases. But that mail address no longer exists I have just updated my current Apple ID with my new e-mail address when I switched to the new ISP.

I think I have seen somewhere that the Apple ID is linked to the app/purchase which is also fine - but since it is the actual e-mail address and not some kind of SID that seems to be a problem when trying to restore the iCloud backup.

Do you know if there is any way to get around this?