I've been seeing this repeatedly this evening: -
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on both macOS and iOS devices.
What was strange was that I was able to log into https://appleid.apple.com/#!&page=signin without problems.
After some trial and error, I realised that, for some reason, my home broadband router was somehow blocking the connection.
I proved this, on an iPhone, by turning off WiFi and using 3G instead. I proved the same on an iPad and on a Mac, by connecting to a different broadband connection.
Weird or what ?