swap_dims does not propagate indexes properly

[dcherian]

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, 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