ENH: Add the `axis` and `ndim` attributes to `np.AxisError` (#19459)

This PR adds the new axis and ndim attributes to the np.AxisError class, an addition inspired by similar
changes introduced to AttributeError in Python 3.10.

It also provided an excuse to update the classes' documentation and tests, both of which were previously rather lacking.


* ENH: Add the `axis` and `ndim` attributes to `np.AxisError`

* MAINT: Let the new `AxisError` attributes survive pickling

* DOC: Update the `AxisError` documentation

* TST: Update the `AxisError` tests

* DOC: Add a release note

* MAINT: Improve the description of `AxisError`s overloaded constructor

* TST: Fix a few typing test failures

* DOC: Clarify a fix a few parts of the `AxisError` docstrings

Co-Authored-By: Eric Wieser <425260+eric-wieser@users.noreply.github.com>

* DOC: Reguide fix

* DOC: Replace `versionadded` with `versionchanged`

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

* DOC: Mention that `AxisError` is a `ValueError` and `IndexError` subclass

Co-Authored-By: Sebastian Berg <sebastian@sipsolutions.net>

* ENH: Delay assembling of the error message until `__str__` is called

Co-Authored-By: Eric Wieser <425260+eric-wieser@users.noreply.github.com>

* DOC: Update the `AxisError` string representation in its docstring

* DOC: Update `versionadded`-related information

Co-Authored-By: Eric Wieser <425260+eric-wieser@users.noreply.github.com>

* DOC: Fix sphinx warnings

Co-authored-by: Eric Wieser <425260+eric-wieser@users.noreply.github.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Sebastian Berg <sebastian@sipsolutions.net>

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