Let concat promote a mix of numpy and pandas extension coord dtypes

[dchaudhari7177]

Fixes #11317

The failure

PandasIndex.concat promotes the coordinate dtypes of the indexes it joins with np.result_type (xarray/core/indexes.py:793), which cannot interpret a pandas extension dtype. Under pandas 3 a string index carries a StringDtype, so the reporter's case has one coord at <U1 and the other at StringDtype and raises:

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

This is not an exotic mix — it is what you get whenever one dimension coordinate came from a pd.Index (which is how concat is documented to add a new labelled dimension) and another from a plain list.

The fix

By the time the dtypes are promoted, _concat_indexes has already built the joined index, and pandas promoted the dtypes to do so. When any input coord dtype is a pd.api.extensions.ExtensionDtype, use the dtype pandas settled on rather than reimplementing its promotion rules here:

elif any(
    isinstance(dtype, pd.api.extensions.ExtensionDtype)
    for dtype in indexes_coord_dtypes
):
    coord_dtype = new_pd_index.dtype

Two numpy dtypes still go through np.result_type unchanged, so ordinary promotion (<U1 + <U3 → <U3) is untouched.

I deliberately did not touch xarray.core.dtypes.result_type, which fails the same way on this pair. Making the general promotion path extension-aware is a larger decision about the pandas-3 string transition and would likely collide with in-flight work such as #11474; this keeps the change to the one site the issue is about.

Verified

• The issue's reproducer now returns a 2-element dim_a with values ['a', 'b'].
• The xr.Variable form the reporter noted still works is unchanged (<U1).
• Red before green: with both new tests in place and indexes.py reverted, test_concat_mixed_numpy_and_extension_coord_dtype fails with the original TypeError, and the numpy-path test passes either way — so it is guarding against the new branch swallowing the ordinary case.
• pytest xarray/tests/test_concat.py xarray/tests/test_indexes.py xarray/tests/test_dataset.py — 680 passed, 59 skipped, 1 xfailed, 1 xpassed.
• ruff check clean at the pinned v0.15.20.

Environment: pandas 3.0.3, numpy 2.x, Windows.

whats-new.rst entry added under Bug fixes.

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