Removes these files that were deprecated since 1.15.0:

- numpy/testing/decorators.py
- numpy/testing/noseclasses.py
- numpy/testing/nosetester.py

This also resolves a failure in the recently introduced tests
in `test_public_api.py` (see gh-14454).  Closes gh-14566

Otherwise the deprecation message is not that helpful as I have to dig
through the source to find out since when and whether conditional import
is necessary in my code. I may not have numpy on my dev machine (this
message was on CI). So it's one extra step for the consumer.

That's also for you, you have more chance of having consumer update
their code when they have more informations in the deprecation message,
so you can drop old code faster !

At least kudo to Charles Harris for including a comments just above,
that prevented me from having to git blame and go spelunking for knowing
which versions were or not affected.

The following modules have been moved or renamed and should not be
imported. This adds shim modules for the old names that issue a
DeprecationWarning on import.

* numpy/core/umath_tests.py
* numpy/testing/decorators.py
* numpy/testing/noseclasses.py
* numpy/testing/nosetester.py
* numpy/testing/utils.py

Closes #10845.

The warning type is the second, not the first, argument.

Downstream projects were importing directly from the testing modules
rather than from testing. Discourage this.

This is to prepare for the switch to pytest.

* Rename `numpy/testing/nose_tools` to `numpy/testing/_private`.
* Redirect imports as needed.
* Copy `_testutils.py` from scipy to `numpy/testing/_private`.
* Rename `_testutils.py` to `_pytester.py` and remove unneeded bits.

The noseclasses module should not be imported by users.

The aim here is to separate out the nose dependent files prior to adding
pytest support. This could be done by adding new files to the general
numpy/testing directory, but I felt that it was to have the relevant
files separated out as it makes it easier to completely remove nose
dependencies when needed.

Many places were accessing submodules in numpy/testing directly, and in
some cases incorrectly. That presented a backwards compatibility
problem. The solution adapted here is to have "dummy" files whose
contents will depend on whether of not pytest is active. That way the
module looks the same as before from the outside.

In the case of numpy itself, direct accesses have been fixed. Having
proper `__all__` lists in the submodules helped in that.