Can't unstack concatenated DataArrays

What happened?

I had a collection of DataArrays with a stacked dimension (dimension whose corresponding index is a MultiIndex). I concatenated them into a single DataArray, then tried to unstack the stacked dimension, which failed. Performing the operations in the other order works (unstacking each DataArray, then concatenating the unstacked arrays).

What did you expect to happen?

I expected that concatenating the arrays then unstacking them would produce the same array as unstacking them then concatenating them, but with the possibility of saving the intermediate concatenated-but-still-stacked DataArray for later use as a template.

Minimal Complete Verifiable Example

import pandas as pd
import xarray
index = pd.MultiIndex.from_product([range(3), range(5)])
arr = xarray.DataArray.from_series(pd.Series(range(15), index=index)).stack(index0=["level_0", "level_1"])
arr.unstack("index0")

arr2 = xarray.concat([arr, arr], dim="index2")
arr2.unstack("index0")

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.

Relevant log output

<xarray.DataArray (level_0: 3, level_1: 5)>
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14]])
Coordinates:
  * level_0  (level_0) int64 0 1 2
  * level_1  (level_1) int64 0 1 2 3 4

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/dataarray.py", line 2402, in unstack
    ds = self._to_temp_dataset().unstack(dim, fill_value, sparse)
  File "~/.conda/envs/plotting/lib/python3.10/site-packages/xarray/core/dataset.py", line 4618, in unstack
    raise ValueError(
ValueError: cannot unstack dimensions that do not have exactly one multi-index: ('index0',)

Anything else we need to know?

The eventual problem to which I wish to apply the solution has two stacked dimensions rather than one, but that's likely irrelevant.

Environment

Start by reproducing the MVCE through DataArray.unstack after concat, then read the DataArray.unstack and Dataset.unstack paths named in the traceback. Compare the result with unstacking before concat; done means the concatenated DataArray can be unstacked consistently, including the reported MultiIndex case.