Airport Express and Time Capsule don't recognise Apple ID any more
Suddenly, my Airport Express and Time Capsule devices no longer can be authenticated by my Apple ID. No change of passwords or AppleID, but I can no longer use the Time Capsule for Time Machine back-ups. Strangely, the Time Capsule's WiFi network kept working, and the Airport Expresses still received audio from my MacBook Pro, which runs the latest MacOS, Mohave 10.14.3.
Both Airport Expresses are good for audio, despite flashing yellow light and the message on Airport Utility that they both have "Unrecognised Apple ID or password".
I then told Airport Utility to forget the Time Capsule, and now it can't be found as "Other WiFi Device". However, as Time Capsule WiFi Network, it reappears in Airport Utility, and works fine connecting to the internet via my modem. But not to back up!
What's going on???