I've found myself at this webpage multiple times while trying to minimize the complexity of APIs in my C projects. I think it does a lovely job explaining control flow and it has helped me to think more explicitly about storage of state on and off the stack as well as the readability consequences of different approaches.

My conclusion for now is that the choice to use C coroutines is best left to the library user. For example: Mongoose (https://github.com/cesanta/mongoose) uses event callbacks to deal with asynchronousness. It is much more pleasant to wrap a library like this in whatever thread/task primitives your system has rather than try to port the mythical cross-platform C couroutine or worse, std::thread.