I can not add one of my email address to my reachable at contact emails list

It shows “could not connect to iCloud the request cannot be processed at this time. Please try again later” after I entered the verification code

I tested that I can add other emails but only this one email can not be added.

And I also tried on many devices (iPhones iPads) and all the same result as said above.

So the issues must be at this email address. But it is a very regular hotmail email and I can receive the verification code fine and I also went to apple.com to use the Forrest password feature to test if this email is used on other Apple ID , and it turned out it has not been used before. So I have no idea what’s the problem with this email. I also contacted the apple support. They tell me to contact the Microsoft ( the email provider)……… at which I believed is not the issue since I can receive the verification code fine.