Fix shift and pad on pandas extension-array variables (#10301)

[MaykThewessen]

What

DataArray/Dataset .shift() and .pad() raise TypeError on variables backed by pandas nullable extension arrays (Int64, Float64, boolean):

import numpy as np, pandas as pd, xarray as xr

arr = pd.Series(index=np.array([1, 2, 3]), data=1).convert_dtypes().to_xarray()
arr.shift(index=1)       # TypeError: int() argument must be ... not 'NAType'
arr.pad(index=(1, 1))    # TypeError: int() argument must be ... not 'NAType'

Both methods route through duck_array_ops.pad → np.pad, which coerces the extension array to a plain numpy array and then cannot insert the pd.NA fill value into an integer/float/bool ndarray. (String-backed arrays accidentally worked because they coerce to object.)

This is the part of #10301 not covered by the merged #10423 (which fixed the NA type-promotion path used by reindex/fillna, but not the padding path).

How

• Register an np.pad NEP-18 handler on PandasExtensionArray (__extension_duck_array__pad). For mode="constant" it builds the padded result from same-dtype extension arrays and concatenates them with _concat_same_type, so the extension dtype and its native pd.NA are preserved. Per-side construction also honors constant_values=(before, after).
• duck_array_ops.pad wraps raw extension arrays in PandasExtensionArray for constant-mode padding (the same idiom already used by as_shared_dtype), so the handler is reached. Non-constant modes (edge, reflect, …) don't introduce fill values and keep the existing numpy path unchanged.

>>> arr.shift(index=1)
<xarray.DataArray (index: 3)> ...
<IntegerArray>
[<NA>, 1, 1]
Length: 3, dtype: Int64

Scope

Intentionally narrow: this only fixes the shift/pad crash and does not attempt the broader ufunc/operator work being explored in #10380. Numeric (Int64/Float64/boolean), as well as categorical and other extension types, are exercised by the tests.

• Closes the shift/pad part of Regression in DataArrays created from Pandas #10301
• Tests added (test_duck_array_ops.py, test_dataarray.py)
• User visible changes documented in whats-new.rst
• New functions/methods are listed in api.rst (internal only)

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_{Authored with AI assistance (Claude), reviewed and verified by me. Happy to adjust the approach, e.g. fold it into #10380 if maintainers prefer a single consolidated fix.}