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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.
1Thanks for documenting your solution for future users :) I've edited out the "spoiler alert" as self-answers are perfectly welcomed (preferred, even!) here and it reads better if questions stand on their own and contain just the question. You should also be able to accept your self-answer in a couple days, effectively marking this question as answered. – Bob – 2019-10-24T01:57:25.420
A slightly different solution (to what I think is the same problem) was posted here: https://superuser.com/questions/1489760/
– jimtut – 2019-10-24T11:36:02.263