To my knowledge there's no historic precedent for what's happening. Times of regrowth in the past after catastrophic decline (such as major war) was generally a

To my knowledge there's no historic precedent for what's happening. Times of regrowth in the past after catastrophic decline (such as major war) was generally already in the context of extremely high fertility rates. What we do have is increasing evidence, across multiple nations such as Iran and China, that it's relatively easy to lower fertility rates and extremely difficult to bring them back up. So I don't think there's any reason to expect a bullwhip type effect. It could simply be that we've created a system which does remarkably well up front, and then catastrophically collapses in the tail-end. If one wants to be especially fatalistic, we could even be looking at the Great Filter of the Fermi Paradox, but I think that's improbable - there still remain many high fertility cultures and they will simply inherit the world as low fertility cultures die off.