I would say that criticizing the documentation is distinct from criticizing the language itself. The Python standard library has had documentation problems for a while now, but realistically so does pretty much every other programming language. If you want to learn how to do things, you need a book.

If you're still interested in the topic, async/await is intended to be single threaded by default, but has some support for pushing jobs off to threads or processes, using a concurrent.futures Executor internally. Normally if I want process parallelism however, I don't bother with async/await and I go for the more explicit solution.

Again, I think there is a very clear sense of the one obvious way to do it in the minds of many python programmers, but it might not be expressed well in the official documentation. This would be a great opportunity to write a book, for example.