This Mac can't connect to iCloud because of a problem with myEmail popup
Chris Haertel's answer to a different question also works here, as evidenced by an Apple Discussions thread:

In your user folder, go to ~/Library/Keychains/ (hold down the option key when clicking in the Go menu in Finder to show the Library folder).
In that folder, there are the regular keychains, plus some folders with monstrously long names like F2555809-AAC0-5CFA-BEF6-57BB56345BIUR or some such.
I deleted those folders only.

After restarting, you may need to log into iCloud again, but the persistent popup and &quot;An unknown error occurred&quot; messages should be gone for good.