Heritability does not imply the existence of a genetic mechanism. Twin studies have a number of flaws that further demonstrate my points about standards of methodology that geneticists wouldn't touch with a ten foot pole. Even not taking into account stuff like equal environment assumption, identical twins simply do not have the same DNA. Yes, even identical twins, look it up. There are also a number of things that are heritable without involving a genetic mechanism at all, such as the various microbiomes or epigenetics. And of course there are things like transmission of de novo mutations over up to two generations (e.g. affecting germinal cells of one's fetus).
Regarding the 'IQ is the best finding we have on psychologist' point. Being the best in a field that's a largely grift doesn't make one any less of a grift. IQ (and g) still has flaws that no one in the hard science would consider it. For instance, it is gaussian for no reason and despite most social outcomes performances being fat-tailed, meaning the theoretical covariance between IQ and any kind of relevant task is undefined (and its in-sample variance finite but meaningless). There's also zero neurological or genetic data confirming the existence of g, making it a purely imaginary construct that only exists in the minds of psychologists. That this is the best they can come up with just speaks even worse of the field as a whole.