How much of that gain is genetic?

I don't know, but if we can see easily >58SDs from a combination of carefully engineered environment and centuries of breeding... And I don't know how much of that is simply being fed nutrient-rich feed, given the doubling of productivity over the past 2 decades, unless dairy farmers only then realized 'oh, we should feed cows more!', which seems unlikely.

That said, even just breeding is now old-fashioned; these days, the cutting edge in cow tech is using genotyping + phenotype data to more accurately estimate 'lifetime net merit' and pick animals to breed (a form of molecular breeding).