Having just conquered this very thing (again) on one of my my own machine's a couple of hours ago (and having done so several times in the last couple of months), I can tell you there's unfortunately not a straightforward "1. But: its not quite as terrible as it seems (in my experience). What's happening is that Apple's tring to implement a "middle ground" approach in not simply breaking iCloud syncing across the board all at once for everyone, so some processes will continue to accept the unpatched authentication tokens, while others require immediate reauthentication. But far more likely is that you're experiencing the fallout of several recent significant changes affecting iCloud authentication across the board, due to several serious security vulnerabilities discovered in the past few months. Its not entirely tied to Mojave per se, nor do I think your theory of "the root cause must be a corrupted state that is kept by iCloud locally as persistent data that resides local to a macOS user account", is it exactly (though it is not outside the realm of possibility). You're absolutely right, this is a very common occurrence right now.
removing what files resets the iCloud client in macOS to a "clean" state? Where does iCloud store such information, i.e.
UPDATE I'm by now pretty certain that the root cause must be a corrupted state that is kept by iCloud locally as persistent data that resides local to a macOS user account. UPDATE I've meanwhile reinstalled macOS Mojave (with Command + R) but the situation is unchanged. Things seemed normal thereafter, but now this issue is showing up, and it may well be related.
Is this a known issue and how can it be overcome? I remember that the macOS upgrade process got permanently stuck (> 1 hour also very annoying!) very late on (after the first login prompt and presumably also were it tried to set up iCloud) and I had to reboot the machine.
cannot see calendar entries previously created there) and have supplied my password in vain. So in effect I am locked out of iCloud (e.g. When I press "Continue", confirm again with "Continue", and supply my Apple ID password, there is some kind of processing going on for a few seconds, but then the system returns to the same point and state. After upgrading to macOS Mojave (10.14) I face this issue: System Preferences / iCloud reports "Update Apple ID Settings: Some account services will not be available until you sign in again".