What happened?

When upgrading to 2022.6.0.rc0 from 2022.3.0 I noticed a possible unexpected breaking change in the Dataset.indexes property. MultiIndices are now listed for each dimension they apply for as well as once for the multi index itself when accessing dataset.indexes.

What did you expect to happen?

Same behaviour as before, see example below.

Minimal Complete Verifiable Example

```Python

execute with 2022.3.0 and 2022.6.0.rc0 to see the differences

import pandas import xarray as xr

def _create_multiindex(**kwargs): return pandas.MultiIndex.from_arrays(list(kwargs.values()), names=kwargs.keys())

ds = xr.Dataset() ds.coords["measurement"] = _create_multiindex( observation=["A", "A", "B", "B"], wavelength=[0.4, 0.5, 0.6, 0.7], stokes=["I", "Q", "I", "I"], )

for name, idx in ds.indexes.items(): print(name, idx) ```

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, returning the result.
• [x] New issue — a search of GitHub Issues suggests this is not a duplicate.

Relevant log output

```Python Output with version 2022.3.0:

measurement MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], names=['observation', 'wavelength', 'stokes'])

Output with version 2022.6.0.rc0:

measurement MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') observation MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') wavelength MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') stokes MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') ```

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS ------------------ commit: None python: 3.8.10 (default, Jan 28 2022, 09:41:12) [GCC 9.3.0] python-bits: 64 OS: Linux OS-release: 5.10.102.1-microsoft-standard-WSL2 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: C.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.10.5 libnetcdf: 4.6.3 xarray: 2022.3.0 pandas: 1.4.3 numpy: 1.23.0 scipy: 1.9.0rc1 netCDF4: 1.5.4 pydap: None h5netcdf: None h5py: 3.7.0 Nio: None zarr: None cftime: 1.6.1 nc_time_axis: None PseudoNetCDF: None rasterio: 1.3b3 cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.5.2 cartopy: 0.19.0.post1 seaborn: None numbagg: None fsspec: None cupy: None pint: None sparse: None setuptools: 56.0.0 pip: 21.3.1 conda: None pytest: 7.1.2 IPython: 8.4.0 sphinx: 4.5.0

INSTALLED VERSIONS ------------------ commit: None python: 3.8.10 (default, Jan 28 2022, 09:41:12) [GCC 9.3.0] python-bits: 64 OS: Linux OS-release: 5.10.102.1-microsoft-standard-WSL2 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: C.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.10.5 libnetcdf: 4.6.3 xarray: 2022.6.0rc0 pandas: 1.4.3 numpy: 1.23.0 scipy: 1.9.0rc1 netCDF4: 1.5.4 pydap: None h5netcdf: None h5py: 3.7.0 Nio: None zarr: None cftime: 1.6.1 nc_time_axis: None PseudoNetCDF: None rasterio: 1.3b3 cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.5.2 cartopy: 0.19.0.post1 seaborn: None numbagg: None fsspec: None cupy: None pint: None sparse: None flox: None numpy_groupies: None setuptools: 56.0.0 pip: 21.3.1 conda: None pytest: 7.1.2 IPython: 8.4.0 sphinx: 4.5.0