It quacks enough to pass inspect.isroutine, which is the best that is possible as far as I can tell, see also gh-23307. Not sure what you are doing, but maybe it also makes sense to use type(np.mean).
This was a Python function type, and isn't anymore, there is nothing more to the change (except of course a huge speedup in dispatching) really everything else drops out from that, whether surprising or not.

Well, we're dispatching based on the type of objects, in this case np.mean, and now this type is a private thing, which indicates we shouldn't be using it. But I think it's reasonable to expect that the type of something like np.mean to be a public kinda thing.

Ah well, I don't mind adding it somewhere, but also don't know a particularly good place that is clearly "public".

numpy.core.ArrayFunctionDispatcher?

I think this type should not be exposed. We should be free to make this kind of change to what is internal infrastructure, so using inspect.isroutine seems much more reasonable than exposing this type.

@rgommers this type is exposed via type(np.mean), and it's exposed the wrong way. I really do think the type of something like np.mean should be public, but even if you decide not to make it public, one should be able to import whatever the output of type(obj) is, and in this case, numpy._ArrayFunctionDispatcher cannot be imported, but is reported to be the type of np.mean. We should at least fix this inconsistency.

With current main:

>>> type(np.mean)
<class 'numpy._ArrayFunctionDispatcher'>
>>> from numpy._core.overrides import _ArrayFunctionDispatcher
>>> type(np.mean) is _ArrayFunctionDispatcher
True
>>> from numpy._core._multiarray_umath import _ArrayFunctionDispatcher
>>> type(np.mean) is _ArrayFunctionDispatcher
True

The __module__ attribute of np.mean is explicitly set to 'numpy' inside the array_function_dispatch decorator. That goes through several layers of decorators and functools.wraps. I don't really know how to unravel that without spending more time than I have for this. If there's an easy way to make type(np.mean) return what you want here, changing that seems okay. I'd say it's very low-prio for us though, since no one really should make use of anything that is private.

this type is exposed via type(np.mean), and it's exposed the wrong way

I would not call that "exposed". Using type like that is very non-idiomatic. inspect.isroutine should do all you need here, there's nothing you can/should do with a private type in Python.

The module is hard-coded in the C type structure, very simple to change for someone who wants to.