Looking at the code: we don't need to use iscoroutinefunction at all.  If we had separate methods for sync and async context managers, you can store the flag if a function is async or sync along with it.

So _exit_callbacks should store tuples `(is_async, cb)`, instead of just `cb`.

asyncio.iscoroutinefunction differs from inspect.iscoroutinefunction a little bit to support asyncio-specific debug coroutine wrapper functions.  We should avoid using any version of iscoroutinefunction here.