Verification Failed: Since updating to macOS Catalina error connecting to Apple server, can’t Sign In with Apple ID

I fixed this having seen a solution to a different problem

System Preferences > Network > and create a new Network Location (normally its says Automatic) and to re-join a known working wi-fi network.

Then log on to iCloud.

MC

sorry to hear it.

I had tried other things as well, maybe it was an accumulation

I signed out of iCloud - it took an age to download the cloud to the computer, in fact I cancelled it and signed out of iCloud.

I restarted the computer (a few times as it happens)

it was a truly frustrating process but the last bit worked

the final bit was System Preferences > Network > and create a new Network Location (normally its says Automatic) and to re-join a known working wi-fi network.

Then log back on to iCloud.