I think you're right about women and birth rates, but I don't think it's anything mystical, rather it's just an unconscious perception

Like that eerie feeling you get when you feel a place 'isn't right', it's usually several red flags you don't even consciously know but your brain is saying 'Ok a lot of things here match with a bad thing that happened in the past, be careful'

And I feel our current and coming economic collapse is creating these subconscious red flags that women intuitively feel:

The necessities for life are more and more difficult to acquire, women's rights to healthcare is being attacked, and authoritarianism which is inherently misogynistic is on the rise

Honestly it just makes sense that women don't want to bring babies into this messed up world.