But, isn't the separation of the control-flow into chunks, either separated by async/await or by sepration between call and callback, a form of cooperative thread yielding on top of preemptive threads? If that isn't true for .NET, then I'd really interested to understand what else it is doing.

No, it is a state machine that generates an instace of a Task from Task Parallel Library, and automates the Run()/Get() invocations from it.

Assuming your type isn't an Awaitable, with magic methods to influence how the compiler actually generates the state machine.