You're making all these assumptions about how the population grows and shrinks on a tiny subset of human history. People are not going to disappear as a species

You're making all these assumptions about how the population grows and shrinks on a tiny subset of human history. People are not going to disappear as a species from social trends like having fewer children. Society will change to accommodate the new status quo and reach an equilibrium, like it has for the entire history of the species. Whatever wipes out humanity, it won't be that.