BUG: lib.infer_type broken for IntervalArray / PeriodArray

While working on #23167, I found a regression in IntervalArray / PeriodArray - I’m guessing it’s related to the whole EA effort. @jorisvandenbossche @TomAugspurger

>>> import pandas as pd
>>> import pandas._libs.lib as lib
>>> s = pd.Series([pd.Period(2013), pd.Period(2018)], dtype='category')
>>> lib.infer_dtype(s.values.categories)
Traceback (most recent call last):
  File "pandas\_libs\lib.pyx", line 1166, in pandas._libs.lib.infer_dtype
    values = getattr(value, '_values', getattr(value, 'values', value))
TypeError: Cannot convert PeriodArray to numpy.ndarray
>>>
>>> t = pd.Series([pd.Interval(0, 1), pd.Interval(0, 2)], dtype='category')
>>> lib.infer_dtype(t.values.categories)
Traceback (most recent call last):
  File "pandas\_libs\lib.pyx", line 1166, in pandas._libs.lib.infer_dtype
    values = getattr(value, '_values', getattr(value, 'values', value))
TypeError: Cannot convert IntervalArray to numpy.ndarray

This was still working in v0.23.4:

>>> import pandas as pd
>>> import pandas._libs.lib as lib
>>> pd.__version__
'0.23.4'
>>> s = pd.Series([pd.Period(2013), pd.Period(2018)], dtype='category')
>>> lib.infer_dtype(s.values.categories)
'period'
>>>
>>> t = pd.Series([pd.Interval(0, 1), pd.Interval(0, 2)], dtype='category')
>>> lib.infer_dtype(t.values.categories)
'interval'

This is due to the fact that lib.infer_dtype tries values = getattr(value, '_values', getattr(value, 'values', value)) and both IntervalArray / PeriodArray do not return a numpy array for _values anymore. For PeriodArray, it would work if _values and values were switched, but for IntervalArray, both _values and values return the same (non-numpy-array) result.

[h-vetinari]

milestone ping pong, haha. 😉

Would this still be acceptable during RC phase? I might be able to make some time.

[jreback]

i think we could eventually add those but the inference is used in indexing so i am not sure if changing it now would work