The few times I've ridden the Thruway service linking OKC and NEW (via Wichita), it was not a Greyhound scheduled route, but a dedicated Amtrak service. It is indeed overnight and uses standard coaches, but only carried Amtrak passengers.
I researched this, as I am booked on this route for later on, and this is one of the hybrid Thruway routes. In other words, it is basically run for Amtrak passengers, but if someone turns up with a connecting Greyhound ticket or walks into their station in the middle of the night to go from Wichita to Newton, they can. The bus company is well-regarded and runs a couple of regular route bus services in addition to the Texas Chief route.
https://www.beeline-express.com/beeline/ does not even show the Oklahoma City -Wichita segment.