Repeated requests to sign into iCloud

On multiple devices (Mac’s, iPads, iPhones) I keep getting notifications that some of my iCloud data is not syncing. This happens several times a day… So I enter my apple iCloud password and the issue temporarily goes away on the device.

More frustratingly, sometimes I am asked to enter the computer (not iCloud) password for one of my obscure Macs. It is an old MBP which I recently revived to update the OS. I could see no reason why I was being asked (many times) to enter the computer password for THAT device on other devices …

So I signed out of iCloud on that MBP, and removed it from my list of apple devices. However, even after doing that I am still being asked to enter its computer password in order to turn on iCloud synch on other devices!

[Edited by Moderator]