In Australia, our supermarket bread almost always has “vegetable oil” in the ingredients. They can’t even be bothered sticking to one type of vegetable oil or listing which ones they use.

I’ll take the home bread

Because they use the oil for how it changes the texture, not for the taste. So corn oil is just as good as soy oil is just as good as canola... and they're going to use whatever is cheapest.

In NZ pretty much every supermarket bakes their own bread which to me seems same like bakery or home bread.