I still don’t understand what a “software factory” is. Can someone clue me in?

You build the system, the factory, that presumably is looking at your task tracker, writes and reviews design docs, reviews code, etc. And this system, in turn, writes software for you.

I don't know how that's supposed to work, but to me it's the most autistic replacement of the actual team that one can come up with.

AIUI, it is a type of factory that produces software.