Cannot export dataset with categorical index in 2025.4.0

What happened?

In 2025.4.0 and on the current master, trying to export to netCDF a dataset created from a dataframe with categorical index raises the error:

TypeError: Cannot interpret 'CategoricalDtype(categories=['C1', 'C2'], ordered=True, categories_dtype=object)' as a data type

What did you expect to happen?

In 2025.3.1 and before, it was possible to export such a dataset (although the categorical index might be lost in the process).

Minimal Complete Verifiable Example

import pandas as pd
import xarray as xr

df = pd.DataFrame([{"ind": "C1", "val": 1.0}, {"ind": "C2", "val": 2.0}]).set_index("ind")
df.index = df.index.astype(pd.CategoricalDtype(categories=["C1", "C2"], ordered=True))
ds = df.to_xarray()

ds.to_netcdf("foo.nc")

MVCE confirmation

• Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• Complete example — the example is self-contained, including all data and the text of any traceback.
• Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

Anything else we need to know?

Might be related to #10301.

Arguably, the new behavior is better than silently converting to another type. But then, the changelog of 2025.4.0 might need a bit more information on how to update your code for this new behavior.

(Cross-ref: https://github.com/capytaine/capytaine/issues/683)

Environment

</details>

Start by running the reported pandas and xarray MVCE through Dataset.to_netcdf and compare it with xarray 2025.3.1. Trace the categorical-index handling involved in export, using #10301 and the cross-reference for context. Done means the example exports successfully again, or the changed behavior is clearly documented with an update path.