id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
2248614324,I_kwDOAMm_X86GByG0,8952,`isel(multi_index_level_name = MultiIndex.level)` corrupts the MultiIndex,2448579,open,0,,,1,2024-04-17T15:41:39Z,2024-04-18T13:14:46Z,,MEMBER,,,,"### What happened?

From https://github.com/pydata/xarray/discussions/8951

if `d` is a MultiIndex-ed dataset with levels `(x, y, z)`, and `m` is a dataset with a single coord `x`
`m.isel(x=d.x)` builds a dataset with a MultiIndex with levels `(y, z)`. This seems like it should work.


cc @benbovy 

### What did you expect to happen?

_No response_

### Minimal Complete Verifiable Example

```Python
import pandas as pd, xarray as xr, numpy as np

xr.set_options(use_flox=True)

test = pd.DataFrame()
test[""x""] = np.arange(100) % 10
test[""y""] = np.arange(100)
test[""z""] = np.arange(100)
test[""v""] = np.arange(100)

d = xr.Dataset.from_dataframe(test)
d = d.set_index(index = [""x"", ""y"", ""z""])
print(d)

m = d.groupby(""x"").mean()
print(m)

print(d.xindexes)
print(m.isel(x=d.x).xindexes)

xr.align(d, m.isel(x=d.x))
#res = d.groupby(""x"") - m
#print(res)
```

```
<xarray.Dataset>
Dimensions:  (index: 100)
Coordinates:
  * index    (index) object MultiIndex
  * x        (index) int64 0 1 2 3 4 5 6 7 8 9 0 1 2 ... 8 9 0 1 2 3 4 5 6 7 8 9
  * y        (index) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99
  * z        (index) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99
Data variables:
    v        (index) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99
<xarray.Dataset>
Dimensions:  (x: 10)
Coordinates:
  * x        (x) int64 0 1 2 3 4 5 6 7 8 9
Data variables:
    v        (x) float64 45.0 46.0 47.0 48.0 49.0 50.0 51.0 52.0 53.0 54.0
Indexes:
  ┌ index    PandasMultiIndex
  │ x
  │ y
  └ z
Indexes:
  ┌ index    PandasMultiIndex
  │ y
  └ z
ValueError...
```

### 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](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [x] New issue — a search of GitHub Issues suggests this is not a duplicate.
- [x] Recent environment — the issue occurs with the latest version of xarray and its dependencies.

### Relevant log output

_No response_

### Anything else we need to know?

_No response_

### Environment

<details>



</details>
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