swap_dims does not propagate indexes properly

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

Start by running the provided xarray example and trace the swap_dims operation, focusing on how unaffected multi-indexes are handled. Use _assert_internal_invariants as the verification point; done means the dataset remains internally valid after swapping the simple indexed dimensions.