Creating a model with "GeneratedField" results in a DoesNotExist error.

Actually, I made a mistake. I missed seeing that both parent classes are abstract. It doesn’t really matter in this case.

I suspect it will. I don’t see anything wrong with the expression that would cause it to fail, provided you’re using the most recent version of Django 5 as suggested above.
(I’d have to try it myself to see.)

I don’t know about MySQL. It won’t in Django unless you’re running 5.1 or apply the patch as described in this thread: Using GeneratedField with Postgres - #2 by felixxm