Hello Sidmouth_Swallows. I had the same issue. Just tried to change my email password. Everything works on all devices except the Mail App on MacBook. After going through many things - logging out of my Apple ID, reinstalling MacOS, etc etc with great support from Apple Technical Support, for me the solution was to create a new log-in on the Mac. Add the email account (internet account), then sign-in to my Apple ID on the new log-in. It was a lot of work, but it seems to be working. I am now trying to restore the precise settings for the full look and feel that I had before the transition on my Mac. I will keep the original log-in account for my Mac until I confirm that new one is working fine. Only real difference noted is that I see two choices for login account when I boot the computer and then I select the new one (which uses the same Apple ID). You may wish to try that.
It seems that there was something amiss with my MacBook account for some reason. But, given how many thousands of Mac users seem to running into similar issues, there is likely a bug that Apple needs to fix somewhere so this is not so regular an occurrence. I will say that I was extremely grateful for the Apple text/phone support on this.