We have 3 sources of difference, genetic heritability, home environment and "others". The things you talk about would go under "others", and they aren't very interesting since we have basically no influence over them, as everything we can influence via nurture goes under home environment and nature via genetic heritage. So for example, of we compare growing up in a rich or a poor household (this includes going to a better school, better neighborhood, better food etc), most of these studies shows that it has almost no effect at all.

You influence "others" by putting your kids in a good school.

It's one of the main drivers of varying housing costs in the US.

School is included in the shared environment because if you had identical twins they would be going to the same school and same classes.

Your parents determines your school, so the quality of your school can't be in "others". The only way school could be in "others" in these studies is if parents often put one twin in a good school and the other twin in a bad school, but I strongly believe that isn't the case.

Your parents don't in all cases. I went to a good school and my brother went to a bad school. My parents didn't choose that. The good school did, it was selective in its students. Selective school aren't all that rare.

In your own words:

> We have 3 sources of difference, genetic heritability, home environment and "others"

Clearly, school is not home environment.

School is determines by your home environment, hence it is a part of the home environment bucket. "other" is not: "everything except home environment and genes", it is: "everything not determined by the home environment or genes".