an independent and officially non-partisan commission is imperfect, but will at least have constraints on it in that it needs to appear independent, unlike the brazenly partisan way things work now.

Are State elections also badly affected by gerrymandering?

I have only ever seen examples of it at the Federal Election level, so wondering if your first point is actually completely accurate. (I believe the States themselves control the "maps" but forgive my ignorance if not)

The states control both maps, the district map which determines the population eligible to elect the US Rep for a given district, and a separate district map (with more and smaller districts) that determines the population eligible to elect the State Rep for a given district.

Both are a problem. The latter just means that the State Congress can be artificially heavily tilted vs one party or the other.