Cannot create Dataset from DataFrame containing CategoricalIndex with Intervals

What happened:
Creating a Dataset from a DataFrame with a CategoricalIndex (where the categories are an IntervalIndex) raises the error:

TypeError: data type not understood

What you expected to happen:
I expected the output to be a Dataset object with the CategoricalIndex as one of the coordinates.

Minimal Complete Verifiable Example:

import pandas as pd
import xarray as xr

df = pd.DataFrame({"name": list("abcdefghijk"), "age": range(11)})
df["age_group"] = pd.cut(df["age"], bins=5)
df = df.set_index(["name", "age_group"])

df.to_xarray()  # or xr.Dataset.from_dataframe(df)

Environment:

Start by running the provided pandas DataFrame example through DataFrame.to_xarray() and xr.Dataset.from_dataframe(). Trace the DataFrame conversion entry point and its handling of a CategoricalIndex whose categories are intervals. Done means both conversions produce a Dataset with the CategoricalIndex represented as a coordinate instead of raising TypeError.