DEPR: masking fallback in binary operations

[jbrockmendel]

ser = pd.Series(['a', np.nan, 'c'], dtype=object)

>>> ser + "b"
0     ab
1    NaN
2     cb
dtype: object

The operation here goes through ops.array_ops where it raises, then falls back to _masked_arith_op where it only operates on non-na entries. This seems mostly motivated by supporting strings-with-nans, but was implemented before StringArray implemented this support (better). Do we still need this fallback behavior?

[jbrockmendel]

xref #41764

[rhshadrach]

I think the proposal here is "NaN + numeric" is still NaN, but "NaN + non-numeric" raises - is that right? +1 if so.

For this, I wonder if we should be treating Boolean values as numeric:

print(np.nan + True)
# nan
print(np.nan + np.array([True])[0])
# nan

[jbrockmendel]

I think the proposal here is "NaN + numeric" is still NaN, but "NaN + non-numeric" raises - is that right? +1 if so.

That's a good way to put it, yes.

[jbrockmendel]

Effectively the same thing for logical ops in na_logical op causes confusion e.g. #40565