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
2228319306,I_kwDOAMm_X86E0XRK,8914,swap_dims does not propagate indexes properly,2448579,open,0,,,0,2024-04-05T15:36:26Z,2024-04-05T15:36:27Z,,MEMBER,,,,"### What happened?

Found by hypothesis
```
import xarray as xr
import numpy as np

var = xr.Variable(dims=""2"", data=np.array(['1970-01-01T00:00:00.000000000', '1970-01-01T00:00:00.000000002', '1970-01-01T00:00:00.000000001'], dtype='datetime64[ns]'))
var1 = xr.Variable(data=np.array([0], dtype=np.uint32), dims=['1'], attrs={})

state = xr.Dataset()
state['2'] = var
state = state.stack({""0"": [""2""]})
state['1'] = var1
state['1_'] = var1#.copy(deep=True)
state = state.swap_dims({""1"": ""1_""})
xr.testing.assertions._assert_internal_invariants(state, False)
```

This swaps simple pandas indexed dims, but the multi-index that is in the dataset and not affected by the swap_dims op ends up broken.

cc @benbovy 

### What did you expect to happen?

_No response_

### Minimal Complete Verifiable Example

_No response_

### 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](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [ ] New issue — a search of GitHub Issues suggests this is not a duplicate.
- [ ] 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>
","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/8914/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,issue