I had a similar issue when I first brought my iPad. Turns out, Apple doesn't like custom domains for emails. So, I had to make an Apple account with a Gmail account, then remove the Gmail account and add my email address with the custom domain.
Why? Who knows. Still remember my first experience after buying an iPad.
You have to reach a human to make a Flickr account in 2025 if you use a custom domain. It wasn't too difficult, they gave me some reason about abuse. Whatever.
Might've had something to do with the state of the various email security measures on the domain. I have an Apple account on a custom domain with Fastmail and it's never been a problem.