repeated request to update Apple ID settings

Please give AppleCare a call, they can help you figure out your problem. By the way, you also may want to seriously consider replacing your 2013 iMac, not only is it obsolete meaning it will not run current versions of Mac OS but Apple classified it as Vintage years ago. Vintage means parts are no longer available.

In the USA, AppleCare's number is 800-275-2273.

Updating your Apple ID settings may require that you login to your Apple ID iCloud account several times on that Catalina iMac.

I have a couple Catalina Macs that do that sometimes if I make changes to my Apple ID configurations on newer Apple devices.

Glad to hear that, your welcome!