API: Add closed to IntervalDtype

[jschendel]

This was brought up by @shoyer in a different issue, and it makes sense to me

Adding closed to IntervalDtype makes sense to me, as in my mind closed is inherently part of the dtype. Since differing closed makes two IntervalIndex incompatible, I'd expect their dtypes to not be equal, but they currently are, which seems a little strange:

In [2]: ii1 = pd.interval_range(0, 3, closed='left')

In [3]: ii2 = pd.interval_range(0, 3, closed='right')

In [4]: ii1.dtype == ii2.dtype
Out[4]: True

There's also a larger discussion as to if adding closed to IntervalDtype would allow us to remove closed as a parameter to the IntervalIndex constructor. My preference would be to keep the closed parameter for user convenience, similar to how CategoricalIndex accepts categories and ordered parameters despite also accepting CategoricalDtype (though maybe this is just for legacy reasons). Willing to be convinced otherwise though.

xref #19263 (comment) (original comment)
xref #19370 (might be rendered moot)

cc @shoyer

[jreback]

+1 on this.

[jbrockmendel]

+1; recent work in implementing validators this would simplify things