This is an extremely well studied and well documented effect. One-off extreme situations such as WWII and COVID aren't counter-examples of a global trend. Development leads to a reduction in fertility. The only dispute globally is what happens once incomes rise after the birth rate falls below replenishment (i.e. whether there's a J-curve effect).

I read your article, and nothing there tracks the correlation between birth rates and income in a greater-than-replenishment situation. I conceded that in the tail end, rising wages may lead to more births, but I have not seen (including in your citations) an indication it would lead to an above-replenishment birth rate. Just some micro-level changes.