In general, I advocate making the API as narrow as possible so:

• let's go with positional-only - there's no need to call axis(arg='off'), and I don't think we can find a much better parameter name here. We can always relax that later if a compelling reason comes up.

• axis(None) is not semantically reasonable. One can prevent that by using a special _DEFAULT sentinel, similar to what we do with UNSET for set():
  

  matplotlib/lib/matplotlib/artist.py

  Lines 90 to 93 in dc0328f

  	class _Unset:
  	def __repr__(self):
  	return "<UNSET>"
  	_UNSET = _Unset()

  (or directly reuse _UNSET, although here the semantics is rather _DEFAULT than _UNSET, so maybe the extra sentinel is semantically justified).
  This is a bit heavy, so I'm really unsure whether accepting None is the pragmatic solution here. OTOH we may have other cases with the same issue and it could be worth making _DEFAULT an explicit concept.

BTW: What is axis() doing anyway? AFAICS this results in set_xlim(None, None, emit=True, auto=None) and likewise for ylim, wich does not change anything. - Maybe we should deprecate an empty axis() call and require either a positional or keyword parameter to be set.

Sure, made it positional only.

axis() with no args is documented to return xmin, xmax, ymin, ymax, which is shorter than calling xlim()/get_xlim() and ylim()/get_ylim() separately; sure, we could deprecate it out of purity but I don't actually think we should -- even if I don't ever use that form, that just seems to be gratuitiously breaking end users (or if we do, we should also get rid of e.g. axis("on")/axis("off") on the grounds that this should be spelled set_axis_on()/set_axis_off()).

Having None be the default and mean the same as no args is pretty standard in Python, and I don't really like the idea of introducing _DEFAULT to strictly keep the same call semantics as previously (for example, distinguishing between None and unset is also the root issue of #24413); Axes.set() is a rather special case as here the signature absolutely cannot be spelled out without introducing such a placeholder.

Maybe we should deprecate an empty axis()

axis returning the limits is a Matlab-ism: https://www.mathworks.com/help/matlab/ref/axis.html

Still a real test failure.

oops, fixed.