use public pandas API instead of pandas.core

[tswast]

The stability of pandas.core is not guaranteed. We should use pandas where we can and raise an issue with pandas where not available.

[jbrockmendel]

I'd also suggest making a PR in pandas to make e.g. NDArrayBackedExtensionArray public

[jbrockmendel]

You might be able to trim some code by using DatetimeLikeArrayMixin instead of NDArrayBackedExtensionArray

[jorisvandenbossche]

To give a few examples, from taking a look at __init__/core.py:

• pandas.core.dtypes.dtypes.register_extension_dtype -> pandas.api.extensions.register_extension_dtype (the same for ExtensionDtype).
• from pandas.core.dtypes.common import is_dtype_equal, is_list_like, pandas_dtype -> from pandas.api.types import is_dtype_equal, is_list_like, pandas_dtype

The pandas.core.nanops.nan... functions have no public alternative at the moment. I am not sure we should expose them somewhere though, so you can maybe just keep those as is (they also haven't changed the last years I think).