BUG: binop methods with `fill_value` not being respected in pandas 2.2

[mroeschke]

BUG: binop methods with `fill_value` not being respected in pandas 2.2

[rohanjain101]

I believe behavior was changed in #55568 but is the 2.2.0 result not the expected result? Since the documentation states that the fill value should only be used when one side is missing, in this case, since the left series is a nullable dtype, should np.nan not be treated as a missing value? I would have thought that even for nullable types, since nan is converted to NA in construction:

>>> pd.Series([np.nan], dtype="Float64")
0    <NA>
dtype: Float64
>>>

In this example, since both left and right are missing values, fill value should not do a replacement.

[sfc-gh-jkew]

The current behavior makes sense (only fill when one side is missing) because it follows the docs, but I can see why this would be confusing. It's entirely reasonable to assume without a close reading that fill_value might fill both sides as opposed to only one side when there's an np.nan.