Basically;
Slaves were forced onto undesirable land cause it what was left
This is not so accurate--heavily Black rural areas often correspond to areas with particularly good soils because they were the most hospitable to plantation agriculture.
Broadly yea, but they didn’t own that land. The only land slaves could actually own after the war (at least in South Carolina) was generally swampy or sea islands. All the good soil was owned by white planters who forced them back into sharecropping slavery
Also true. And explains, even aside from slavery, why these areas are exceptionally rural: Landholding is very concentrated, so there are relatively few smallholder farmers, meaning lower rural populations, especially with the mechanization of agricultural requiring fewer workers. Other rural areas usually have more small farms and higher populations as a result because of the stickiness of owning a farm (much less likely to pick up and move away if your family owns the farm than if you're just a sharecropper or a farmhand).