[SPARK-56122][PS] Use pandas-aware numeric dtype check in Series.cov

[ueshin]

What changes were proposed in this pull request?

This PR updates pyspark.pandas.Series.cov to use pandas' is_numeric_dtype instead of np.issubdtype(..., np.number) when validating the input Series dtypes.

The previous NumPy-based check works for plain NumPy dtypes, but it raises a TypeError for pandas extension dtypes such as StringDtype, which causes Series.cov to fail before it reaches the intended unsupported dtype error path.

This PR also updates the related Series.cov tests to:

• accept the dtype name shown by both pandas 2 (object) and pandas 3 (str) for non-numeric string inputs
• add extension dtype coverage for nullable Float64
• add a string extension dtype case using pandas "string"

Why are the changes needed?

With pandas 3, Series(["a", "b", "c"]).dtype is a pandas extension dtype (StringDtype), and np.issubdtype(self.dtype, np.number) raises:

TypeError: Cannot interpret '<StringDtype(na_value=nan)>' as a data type

That means Series.cov fails in dtype validation instead of returning the expected TypeError("unsupported dtype: ...").

Using is_numeric_dtype is more appropriate here because it is pandas-aware and works with both NumPy dtypes and pandas extension dtypes. This keeps the existing behavior for numeric inputs while making the validation path robust across pandas versions.

Does this PR introduce any user-facing change?

Yes.

For pandas extension dtypes such as pandas 3 string dtype, pyspark.pandas.Series.cov now raises the intended TypeError("unsupported dtype: ...") instead of failing earlier with a NumPy dtype interpretation error.

How was this patch tested?

Added the related tests and the other existing tests should pass.

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

Generated-by: OpenAI Codex GPT-5

[ueshin]

cc @gaogaotiantian @HyukjinKwon @zhengruifeng

[dongjoon-hyun]

Merged to master. Thank you, @ueshin .