Can’t add phone number to my EA account – “Something went wrong” error

When I try to add a phone number to my EA account, I get the following error message:

Something went wrong. Try again later.

I’ve already contacted EA support, but they couldn’t fix the issue.
I’ve tried adding different phone numbers – none of them work.
On my other EA account, adding a phone number works without any problems.

Has anyone experienced this issue and found a solution?