This is a clever idea but I doubt it's worth adding.
The pattern proposed in the example in the first post doesn't strike me as very readable -- though you don't give any examples of *using* the decorator from the example, so it's a little difficult to imagine what the use case would be.
Adding __parent__ would have to happen as an extra pass once the class is defined -- the decorator (at least its outer part) runs at the time that the method is being defined as a plain function object, and at that time the class object hasn't been created yet. This also means that some decorators can't use the __parent__ attribute (because the outer function of the decorator runs before the object to be stored in __parent__ has been created).
If you really want to explore this idea further, you can probably define a metaclass that adds a __parent__ attribute to the function objects in the class __dict__ when the class is being created. Then you can experiment with using the pattern in some real code. Please report back here with some examples where the presence of __parent__ lets you write cleaner code.
An alternative that wouldn't even require a metaclass would be to write a helper function that looks the class object up by name after parsing __qualname__. There are some limitations to this, e.g. classes defined inside functions -- but that's already a suspect pattern anyway.