Again, that's not how our modern understanding of genomics works, and hasn't been since the 1980's. There's much, much more to it than genes+environment. See all the mechanisms I've mentioned in GP. Also, you brought up 'variation between people', which can be aditionnally confounded by things that have nothing to do with DNA at all, such as the various microbiomes.

It's important to note that heritability is not some kind of magic bullet that explains everything with "genes". If you want to convince a biologist that "genes" are the cause for a given phenotype, you've got to show an actual genetic causal mechanism or you've got nothing. This is, again, due to the myriad of interfering mechanisms that make "genes" very, very removed from the actual phenotype. And again, I'm not talking about the environment.

It's worth noting that there are two uses of gene here, or at least of "genetic".

One of which is roughly DNA that codes for a protein, or controls such, and indeed the causal mechanisms from there to phenotype can be extremely complicated and hard to figure out.

In the context of "variation between people" there's another meaning, of just whatever it is that causes inheritance. We could say many things about this (e.g. from twin studies) even before we'd discovered DNA, and non-DNA routes (like if most babies get some microbes from their mothers) would still count.

The complexity of how biological mechanisms work does not change basic facts about genetics. There isn't any conflict between the two.

Your second point is not true for complex polygenic traits like height. Height is strongly influenced by genetics but we will likely never understand the exact mechanisms that do this.