Comment by HendrikHensen

You're right, it looks like these days you have to fill in an email address. Though any random thing can be filled in. They will send a verification code, and on the next screen you can either fill it in or click Skip in top right. Then in the preferences, it can be removed from the account. A bit annoying for sure, but still not valid email address needed.

But it is true that at any time they could make using an email address or phone number mandatory, and then creating an Advent of Code account will be gated behind that.