BUG/API: floordiv by zero in Int64Dtype

[jbrockmendel]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

ser = pd.Series([0, 1])
ser2 = ser.astype("Int64")

>>> ser // 0
0    NaN
1    inf
dtype: float64

>>> ser2 // 0
0    0
1    0
dtype: Int64

# with int64[pyarrow] this just raises pyarrow.lib.ArrowInvalid: divide by zero

Issue Description

We patch the results of floordiv in dispatch_fill_zeros, but don't do this for the masked dtypes, and the pyarrow one raises.

Expected Behavior

Ideally these would be consistent across backends.

Installed Versions

Replace this line with the output of pd.show_versions()

[manikrishna-m]

take

[jbrockmendel]

Closing as duplicate of #30188