For what it’s worth, studies on schizophrenia and on relatives-of-people-with-schizophrenia showed the least evidence of this problem, while autism was terrible, with 4 times as many significant papers as expected by chance. I’m not sure this is worth much, though. We don’t know if this tells us more about schizophrenia vs autism, or more about the researchers that study them.
Anyway, this is an important study, and the inverse power calculation approach is certainly a useful one. It’s not new, but it’s not used as widely as it ought to be. It does make the assumption that the meta-analyses are “right” about the effect size, and then paradoxically concludes that they are biased. However, this means that the true bias is probably even bigger than this suggests (because if the analyses as biased, the true effect size is smaller than assumed, and the studies should have been even less likely to find it.)