Indexing a RangeIndexed' DataArray with a RangeIndex returns a deprecated Int64Index

What happened?

First, apology if this is not actually a bug - I'm not too sure of what the intended behaviour should be. But I find this counter-intuitive.

When indexing a DataArray that is indexed using a RangeIndex, the resulting index is an Int64Index:

my_da.get_index('time')
>>> RangeIndex(start=0, stop=100, step=1, name='time')

a = my_da.sel({'time': pd.RangeIndex(0,2)})
a.get_index('time')
>>> Int64Index([0, 1], dtype='int64', name='time')

Setting the index to the desired RangeIndex using assign_coords() then works. But I find it a bit problematic that sel() returns an Int64Index even when used with a RangeIndex. Also because Int64Index has been recently deprecated in Pandas 1.4.

What did you expect to happen?

I would have expected the resulting DataArray to be indexed with the same RangeIndex used in sel().

Minimal Complete Verifiable Example

import xarray as xr
import numpy as np
import pandas as pd

my_da = xr.DataArray(np.random.rand(100,),
                     dims=('time'),
                     coords={'time': pd.RangeIndex(0, 100)})

print(my_da.get_index('time'))
a = my_da.sel({'time': pd.RangeIndex(0,2)})
print(a.get_index('time'))

Relevant log output

RangeIndex(start=0, stop=100, step=1, name='time')
Int64Index([0, 1], dtype='int64', name='time')

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS

commit: None
python: 3.8.5 (default, Sep 4 2020, 02:22:02)
[Clang 10.0.0 ]
python-bits: 64
OS: Darwin
OS-release: 20.6.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: None
LOCALE: (None, 'UTF-8')
libhdf5: None
libnetcdf: None

xarray: 0.20.2
pandas: 1.4.0
numpy: 1.22.1
scipy: 1.7.3
netCDF4: None
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: None
dask: None
distributed: None
matplotlib: 3.5.1
cartopy: None
seaborn: None
numbagg: None
fsspec: 2021.11.1
cupy: None
pint: None
sparse: None
setuptools: 59.5.0
pip: 21.3.1
conda: None
pytest: 6.2.5
IPython: 8.0.1
sphinx: 4.3.2

Start with the minimal example using DataArray.sel() and get_index(), then trace how selecting with a pandas RangeIndex produces the result. Done means the selected DataArray preserves the RangeIndex used for selection rather than returning a deprecated Int64Index, with a regression test for the example.