Apple Watch Unlock your Mac Requires Verification that Doesn't Work and Freezes

There seems to be a problem with not the Apple Watch part, but with the iCloud/2-factor authorization part. Note that I have 2-factor authorization on and working on 3 devices (iMac, iPhone, iPad).

System Prefs shows this:

Clicking the "allow Apple Watch to unlock your Mac" results in this:

Open iCloud results in this:

Entering this password results in it asking this:

It then goes to this:

Except none of my other devices get an approval notice. The window just sits there forever. Note that these devices do send approvals to each other and they do send them to my iMac in other scenarios that require 2-factor. The iMac, in this particular case, is just not sending any out to them.

If I hit cancel, the button does nothing and the window remains

If I hit "Can't Approve?" system preferences eventually stops responding and I have to force quit to make the window go away.

I've tried logging in and out of iCloud on all my devices, but it doesn't seem to help.