I'm happy to report that this issue is resolved! Per the advice I got here I contacted FastMail support &, after sending them screenshots of the nag pop-ups, they had me check Opera's "Mail & Chat Accounts..." [from "Tools"]. Sure enough, my wife's email address was there although it didn't belong there. I deleted it & that resolved the problem. Apparently my wife accidentally put her email address there when she responded to a pop-up dialog box that she probably got after hitting the wrong key combination. Thanks for your efforts.
Opera for Linux