Why can't I just sign in without having to either change my password or change my (20 year old) Apple ID?

I'm trying to log in to my iCloud. But Apple has made it so confusing that nothing works anymore. It says I have to verify my email (which has always been xx@mac.com), but that mail doesn't arrive in my Mail app. So I change it to my @me.com or @icloud.com, but Apple says NO.

Everytime I try something made by (new) Apple, everything stops working. Why is this company so useless at helping decadeslong customers?