When I enabled ScreenTime on my MacOS after upgrading to Catalina, and checked "Share across devices" to combine ScreenTime statistics with those on my iPhone, it automatically started to use the ScreenTime passcode I use on my iPhone. The problem: a year ago I had intentionally set a random passcode on my iPhone and forgotten it, figuring that I could always use my laptop to respond to emergencies, and had carefully chosen which apps should always be available. (Furthermore, at some point I managed to disable ScreenTime without even knowing that passcode, so it was disabled when I enabled it on my Mac.)
My Mac was now protected by a passcode I didn't know, and the ScreenTime passcodes apparently act as root-level unbreakable passcodes that brick your computer if you forget them – there is no reset, no override, and no warning. I should note that my Mac never asked me to confirm I knew the passcode it was applying, which it got from my phone while ScreenTime was disabled there, and which I hadn't entered in a year.
Best Answer
The solution
My laptop used my phone's passcode because the ScreenTime passcode appears to be stored in iCloud. Any device that uses ScreenTime will automatically grab and use the ScreenTime passcode stored in iCloud if you enable "share across devices". This even overwrites any passcode set locally, if you later "share across devices."
The way that I recovered my bricked device was to log out of iCloud. This reset all settings connected to iCloud, including ScreenTime. I turned ScreenTime off, logged back into iCloud, and my ScreenTime did not have a passcode and the "Share across devices" box was unchecked. I am treating that box like the nuclear button it is.