The referred twitter OP that gives an overview of the paper also referred to the methodology (and other) criticisms of the paper made by demographer Lyman Stone:
https://lymanstone.substack.com/i/189073871/but-didnt-the-new-study-show-womens-wages-reduce-fertility
Are there possibly any credible responses to the criticisms?
Not trolling in any way once again, I'm basically out of context here: this complicated paper is from a field of study I'm not familiar with.