BUG: Fix Series comparison fails when index dtypes differ (object vs string) (#61099)

[MayurKishorKumar]

• closes BUG: Can only compare identically-labeled Series objects (string vs. object) #61099
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/v3.0.0.rst file if fixing a bug or adding a new feature.

[rhshadrach]

@MayurKishorKumar - looks like your environment got added to your commit.

[MayurKishorKumar]

Oh shoot, my bad! I’ll fix that right away. Thanks for catching it!

[MayurKishorKumar]

Hi @rhshadrach 👋

I’m working on fixing [#61099] and ran into a failure in test_mixed_col_index_dtype.

My fix updates Index.equals so that StringDtype and object dtypes are treated as equivalent when comparing column indexes. As a result, this test now fails because result.columns.dtype becomes "string" while expected.columns.dtype remains object.

There are two options I’m considering:

1. Update the test to explicitly cast expected.columns to "string" when using_infer_string=True, so it reflects the result.
2. Adjust internal logic so the result stays object, but that might go against the spirit of treating string/object as equal.

Would updating the test be acceptable in this case?

Thanks!

[MayurKishorKumar]

pre-commit.ci autofix