BUG: Index.get_indexer will change behaviour for nulls with arrow strings #55833
Description
Pandas version checks
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I have confirmed this bug exists on the latest version of pandas.
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I have confirmed this bug exists on the main branch of pandas.
Reproducible Example
idx = pd.Index(["a", "b", None], dtype="string[pyarrow_numpy]")
idx.get_indexer([None])Issue Description
This returns -1 for the new arrow string dtype because we cast None to np.nan when creating the array. We wanted to be as close to object dtype as possible, but patching this does not seem ideal. Thoughts?
Expected Behavior
see above
Installed Versions
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