I’m originally from Kansas City, and know a number of people from Oklahoma. We all refer to these areas as “the midwest”, because, well, they are. Don’t get hung up on “the plains” or any of that nonsense - “the midwest” is a demographic description, not a geographic one. People in Kansas, Nebraska, Oklahoma, north Texas, Iowa, etc. all very much identify with being from the midwest, because once you get bogged down in the cookie-cutter suburbia, it’s all pretty much identical.
Anyway, calling Oklahoma “the South” is definitely in error. They most certainly don’t self-identify with that.