> Maybe someone knows — assuming birth rates stabilize, albeit lower, do things also stabilize in society a generation after that?

No! Read the article. Birth rates can go extremely low (<0.5), and a society with fertility <2 goes gets exponentially smaller with each generation.

Well, at some population level, the world will not be able to maintain the current technology level. At that point, we will start losing technologies. Once we lose birth control pills (and maybe estrogenoids), I expect the population drop will stabilize - but the world will be at a much lower technology level than it is at today.

Emdash. I see it everywhere now that I know to look for it.