[SPARK-55625][PS] Fix StringOps to make str dtype work properly

[ueshin]

What changes were proposed in this pull request?

Fix StringOps to make str dtype work properly.

Why are the changes needed?

In pandas 3, the default dtype for string is now str or StringDtype(na_value=np.nan).
This is one of extension dtypes, but actually handled as if non-extension dtypes.

>>> pser = pd.Series(["x", "y", "z", None])
>>> other_pser = pd.Series([None, "z", "y", "x"])

• pandas 2

>>> pser
0       x
1       y
2       z
3    None
dtype: object
>>> other_pser
0    None
1       z
2       y
3       x
dtype: object
>>> pser == other_pser
0    False
1    False
2    False
3    False
dtype: bool

• pandas 3

>>> pser
0      x
1      y
2      z
3    NaN
dtype: str
>>> other_pser
0    NaN
1      z
2      y
3      x
dtype: str
>>> pser == other_pser
0    False
1    False
2    False
3    False
dtype: bool

Does this PR introduce any user-facing change?

Yes, it will behave more like pandas 3.

How was this patch tested?

The existing tests should pass.

Was this patch authored or co-authored using generative AI tooling?

No.

[ueshin]

cc @gaogaotiantian @HyukjinKwon @zhengruifeng