Update

Check recent numpy versions for a new typing module

https://numpy.org/doc/stable/reference/typing.html#module-numpy.typing

dated answer

It looks like typing module was developed at:

https://github.com/python/typing

The main numpy repository is at

https://github.com/numpy/numpy

Python bugs and commits can be tracked at

http://bugs.python.org/

The usual way of adding a feature is to fork the main repository, develop the feature till it is bomb proof, and then submit a pull request. Obviously at various points in the process you want feedback from other developers. If you can't do the development yourself, then you have to convince someone else that it is a worthwhile project.

cython has a form of annotations, which it uses to generate efficient C code.

You referenced the array-like paragraph in numpy documentation. Note its typing information:

A simple way to find out if the object can be converted to a numpy array using array() is simply to try it interactively and see if it works! (The Python Way).

In other words the numpy developers refuse to be pinned down. They don't, or can't, describe in words what kinds of objects can or cannot be converted to np.ndarray.

In [586]: np.array({'test':1})   # a dictionary
Out[586]: array({'test': 1}, dtype=object)

In [587]: np.array(['one','two'])  # a list
Out[587]: 
array(['one', 'two'], 
      dtype='<U3')

In [589]: np.array({'one','two'})  # a set
Out[589]: array({'one', 'two'}, dtype=object)

For your own functions, an annotation like

def foo(x: np.ndarray) -> np.ndarray:

works. Of course if your function ends up calling some numpy function that passes its argument through asanyarray (as many do), such an annotation would be incomplete, since your input could be a list, or np.matrix, etc.

When evaluating this question and answer, pay attention to the date. 484 was a relatively new PEP back then, and code to make use of it for standard Python still in development. But it looks like the links provided are still valid.