Fix NA semantics for numpy.StringDType

### What happened?

`StringDType()` with `na_object=np.nan` and `na_object=None` is only partially or not supported.

### What did you expect to happen?

Similar behavior to python object strings

### Minimal Complete Verifiable Example

```Python
# /// script
# requires-python = ">=3.11"
# dependencies = [
#   "xarray[complete]@git+https://github.com/pydata/xarray.git@main",
# ]
# ///
#
# This script automatically imports the development branch of xarray to check for issues.
# Please delete this header if you have _not_ tested this script with `uv run`!

import xarray as xr
xr.show_versions()
# your reproducer code ...
"""
Check how xarray handles NumPy StringDType with different na_object values.

It compares:
  - object-typed DataArray / Dataset (baseline)
  - StringDType-typed DataArray / Dataset (under test)

For each case it runs:
  - .isnull()
  - .count()
  - .dropna(dim="x")
  - .where(~isnull, other="filled")

and records success / failure (with the error message, including na_object).
"""

from __future__ import annotations

import numpy as np
import xarray as xr
from numpy.dtypes import StringDType
from textwrap import shorten

NA_OBJECTS = [np.nan, None]
OPS = ["isnull", "count", "dropna", "where"]


def _short(obj, width=40):
    return shorten(repr(obj), width=width, placeholder="…")


def run_op(kind: str, da_or_var: xr.DataArray):
    """
    Run the four operations on a DataArray (or Dataset variable) and
    return a dict: {op_name: (ok: bool, detail: str)}.
    """
    results: dict[str, tuple[bool, str]] = {}

    # isnull
    try:
        res = da_or_var.isnull()
        results["isnull"] = (True, f"mask={_short(res.values)}")
    except Exception as e:  # noqa: BLE001
        results["isnull"] = (False, f"{type(e).__name__}: {_short(e)}")

    # count
    try:
        res = da_or_var.count()
        results["count"] = (True, f"value={_short(res.values)}")
    except Exception as e:  # noqa: BLE001
        results["count"] = (False, f"{type(e).__name__}: {_short(e)}")

    # dropna
    try:
        res = da_or_var.dropna(dim="x")
        results["dropna"] = (True, f"values={_short(res.values)}")
    except Exception as e:  # noqa: BLE001
        results["dropna"] = (False, f"{type(e).__name__}: {_short(e)}")

    # where(~isnull, "filled")
    try:
        mask = da_or_var.isnull()
        res = da_or_var.where(~mask, other="filled")
        results["where"] = (True, f"values={_short(res.values)}")
    except Exception as e:  # noqa: BLE001
        results["where"] = (False, f"{type(e).__name__}: {_short(e)}")

    return results


def print_case_header(title: str, arr: np.ndarray, dtype, na_obj):
    print(f"\n=== {title} ===")
    print(f"  storage dtype: {dtype!r} (type={type(dtype)})")
    print(f"  na_object: {na_obj!r}")
    print(f"  values: {arr!r}")


def print_results_table(results: dict[str, tuple[bool, str]]):
    # Simple ASCII table: op | OK/FAIL | detail
    col_op = max(len("op"), max(len(op) for op in OPS))
    col_ok = len("status")
    col_detail = 60

    header = f"  {'op'.ljust(col_op)}  {'status'.ljust(col_ok)}  detail"
    sep = "  " + "-" * col_op + "  " + "-" * col_ok + "  " + "-" * col_detail
    print(header)
    print(sep)

    for op in OPS:
        ok, detail = results[op]
        status = "OK" if ok else "FAIL"
        print(f"  {op.ljust(col_op)}  {status.ljust(col_ok)}  {_short(detail, col_detail)}")


def main():
    print("NumPy version:", np.__version__)
    print("xarray version:", xr.__version__)
    print("============================================================")

    summary_rows = []

    # 1) Baseline: object dtype (no custom na_object)
    arr_obj = np.array(["a", np.nan, "c"], dtype=object)

    # DataArray baseline
    da_obj = xr.DataArray(arr_obj, dims="x", name="str_obj")
    print_case_header("DataArray – object dtype (baseline)", da_obj.values, da_obj.dtype, na_obj=None)
    res_da_obj = run_op("DataArray-object", da_obj)
    print_results_table(res_da_obj)
    summary_rows.append(
        ("DataArray", "object", "-", sum(r[0] for r in res_da_obj.values()), sum(not r[0] for r in res_da_obj.values()))
    )

    # Dataset baseline
    ds_obj = xr.Dataset({"str": ("x", arr_obj)})
    var_obj = ds_obj["str"]
    print_case_header("Dataset['str'] – object dtype (baseline)", var_obj.values, var_obj.dtype, na_obj=None)
    res_ds_obj = run_op("Dataset-object", var_obj)
    print_results_table(res_ds_obj)
    summary_rows.append(
        ("Dataset['str']", "object", "-", sum(r[0] for r in res_ds_obj.values()), sum(not r[0] for r in res_ds_obj.values()))
    )

    # 2) StringDType with different na_object values
    for na_obj in NA_OBJECTS:
        dt = StringDType(na_object=na_obj)
        arr_str = np.array(["a", na_obj, "c"], dtype=dt)

        # DataArray with StringDType
        da_str = xr.DataArray(arr_str, dims="x", name=f"str_StringDType_{type(na_obj).__name__}")
        print_case_header(f"DataArray – StringDType(na_object={na_obj!r})", da_str.values, da_str.dtype, na_obj)
        res_da_str = run_op("DataArray-StringDType", da_str)
        print_results_table(res_da_str)
        summary_rows.append(
            (
                "DataArray",
                "StringDType",
                repr(na_obj),
                sum(r[0] for r in res_da_str.values()),
                sum(not r[0] for r in res_da_str.values()),
            )
        )

        # Dataset with StringDType
        ds_str = xr.Dataset({"str": ("x", arr_str)})
        var_str = ds_str["str"]
        print_case_header(
            f"Dataset['str'] – StringDType(na_object={na_obj!r})",
            var_str.values,
            var_str.dtype,
            na_obj,
        )
        res_ds_str = run_op("Dataset-StringDType", var_str)
        print_results_table(res_ds_str)
        summary_rows.append(
            (
                "Dataset['str']",
                "StringDType",
                repr(na_obj),
                sum(r[0] for r in res_ds_str.values()),
                sum(not r[0] for r in res_ds_str.values()),
            )
        )

    # Summary matrix
    print("\n==================== SUMMARY ====================")
    col_scope = max(len("scope"), max(len(r[0]) for r in summary_rows))
    col_storage = max(len("storage"), max(len(r[1]) for r in summary_rows))
    col_naobj = max(len("na_object"), max(len(r[2]) for r in summary_rows))

    header = (
        f"{'scope'.ljust(col_scope)}  "
        f"{'storage'.ljust(col_storage)}  "
        f"{'na_object'.ljust(col_naobj)}  "
        f"{'#OK':>3}  "
        f"{'#FAIL':>5}"
    )
    sep = "-" * len(header)
    print(header)
    print(sep)
    for scope, storage, na_obj_repr, ok_count, fail_count in summary_rows:
        print(
            f"{scope.ljust(col_scope)}  "
            f"{storage.ljust(col_storage)}  "
            f"{na_obj_repr.ljust(col_naobj)}  "
            f"{ok_count:>3}  "
            f"{fail_count:>5}"
        )


if __name__ == "__main__":
    main()
```

### Steps to reproduce

_No response_

### MVCE confirmation

- [x] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [x] Complete example — the example is self-contained, including all data and the text of any traceback.
- [x] Verifiable example — the example copy & pastes into an IPython prompt or [Binder notebook](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [x] New issue — a search of GitHub Issues suggests this is not a duplicate.
- [x] Recent environment — the issue occurs with the latest version of xarray and its dependencies.

### Relevant log output

```Python
NumPy version: 2.3.5                                                                                                                                                                                                                                                                                                  
xarray version: 2025.11.0
============================================================

=== DataArray – object dtype (baseline) ===
  storage dtype: dtype('O') (type=<class 'numpy.dtypes.ObjectDType'>)
  na_object: None
  values: array(['a', nan, 'c'], dtype=object)
  op      status  detail
  ------  ------  ------------------------------------------------------------
  isnull  OK      'mask=array([False, True, False])'
  count   OK      'value=array(2)'
  dropna  OK      "values=array(['a', 'c'], dtype=object)"
  where   OK      "values=array(['a', 'filled', 'c'],…"

=== Dataset['str'] – object dtype (baseline) ===
  storage dtype: dtype('O') (type=<class 'numpy.dtypes.ObjectDType'>)
  na_object: None
  values: array(['a', nan, 'c'], dtype=object)
  op      status  detail
  ------  ------  ------------------------------------------------------------
  isnull  OK      'mask=array([False, True, False])'
  count   OK      'value=array(2)'
  dropna  OK      "values=array(['a', 'c'], dtype=object)"
  where   OK      "values=array(['a', 'filled', 'c'],…"

=== DataArray – StringDType(na_object=nan) ===
  storage dtype: StringDType(na_object=nan) (type=<class 'numpy.dtypes.StringDType'>)
  na_object: nan
  values: array(['a', nan, 'c'], dtype=StringDType(na_object=nan))
  op      status  detail
  ------  ------  ------------------------------------------------------------
  isnull  FAIL    'TypeError: TypeError("dtype argument must be a…'
  count   FAIL    'TypeError: TypeError("dtype argument must be a…'
  dropna  FAIL    'TypeError: TypeError("dtype argument must be a…'
  where   FAIL    'TypeError: TypeError("dtype argument must be a…'

=== Dataset['str'] – StringDType(na_object=nan) ===
  storage dtype: StringDType(na_object=nan) (type=<class 'numpy.dtypes.StringDType'>)
  na_object: nan
  values: array(['a', nan, 'c'], dtype=StringDType(na_object=nan))
  op      status  detail
  ------  ------  ------------------------------------------------------------
  isnull  FAIL    'TypeError: TypeError("dtype argument must be a…'
  count   FAIL    'TypeError: TypeError("dtype argument must be a…'
  dropna  FAIL    'TypeError: TypeError("dtype argument must be a…'
  where   FAIL    'TypeError: TypeError("dtype argument must be a…'

=== DataArray – StringDType(na_object=None) ===
  storage dtype: StringDType(na_object=None) (type=<class 'numpy.dtypes.StringDType'>)
  na_object: None
  values: array(['a', None, 'c'], dtype=StringDType(na_object=None))
  op      status  detail
  ------  ------  ------------------------------------------------------------
  isnull  FAIL    'TypeError: TypeError("dtype argument must be a…'
  count   FAIL    'TypeError: TypeError("dtype argument must be a…'
  dropna  FAIL    'TypeError: TypeError("dtype argument must be a…'
  where   FAIL    'TypeError: TypeError("dtype argument must be a…'

=== Dataset['str'] – StringDType(na_object=None) ===
  storage dtype: StringDType(na_object=None) (type=<class 'numpy.dtypes.StringDType'>)
  na_object: None
  values: array(['a', None, 'c'], dtype=StringDType(na_object=None))
  op      status  detail
  ------  ------  ------------------------------------------------------------
  isnull  FAIL    'TypeError: TypeError("dtype argument must be a…'
  count   FAIL    'TypeError: TypeError("dtype argument must be a…'
  dropna  FAIL    'TypeError: TypeError("dtype argument must be a…'
  where   FAIL    'TypeError: TypeError("dtype argument must be a…'

==================== SUMMARY ====================
scope           storage      na_object  #OK  #FAIL
--------------------------------------------------
DataArray       object       -            4      0
Dataset['str']  object       -            4      0
DataArray       StringDType  nan          0      4
Dataset['str']  StringDType  nan          0      4
DataArray       StringDType  None         0      4
Dataset['str']  StringDType  None         0      4
```

### Anything else we need to know?

_No response_

### Environment

<details>
NumPy version: 2.3.5                                                                                                                                                                                                                                                                                                  
xarray version: 2025.11.0
</details>


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Uh oh!

Fix NA semantics for numpy.StringDType #10967

What happened?

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Minimal Complete Verifiable Example

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Uh oh!

Fix NA semantics for numpy.StringDType #10967

Description

What happened?

What did you expect to happen?

Minimal Complete Verifiable Example

Steps to reproduce

MVCE confirmation

Relevant log output

Anything else we need to know?

Environment

Metadata

Metadata

Assignees

Labels

Type

Projects

Milestone

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Development

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