sel by slice not working for multi-index containing float-values

What happened?

da = xr.DataArray(np.random.rand(4), {'x': np.arange(4)})
da = da.assign_coords(y=('x', np.linspace(0, 1, 4)))
da = da.assign_coords(z=('x', np.arange(4) + 4))
da.set_index(x=["y", "z"]).sel(y=slice(None, 0.5))

fails with

TypeError: float() argument must be a string or a real number, not 'slice'

What did you expect to happen?

In v2022.3, this yields the correct sliced selection. Also, in v2022.6 this works for Multiindices without float-Values

da = xr.DataArray(np.random.rand(4), {'x': np.arange(4)})
da = da.assign_coords(y=('x', np.arange(4)))
da = da.assign_coords(z=('x', np.arange(4) + 4))
da.set_index(x=["y", "z"]).sel(y=slice(None, 2), z=slice(5, None))

(only that the resulting coordinates look a bit weird, containing slices). Also, the sliced selection for a regular float-based index works in v2202.6

da = xr.DataArray(np.random.rand(4), {'x': np.linspace(0, 1, 4)})
da.sel(x=slice(None, 0.5))

Minimal Complete Verifiable Example

import numpy as np
import xarray as xr

da = xr.DataArray(np.random.rand(4), {'x': np.arange(4)})
da = da.assign_coords(y=('x', np.linspace(0, 1, 4)))
da = da.assign_coords(z=('x', np.arange(4) + 4))
da.set_index(x=["y", "z"]).sel(y=slice(None, 0.5))

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

File c:\mambaforge\envs\dev\lib\site-packages\xarray\core\dataarray.py:1420, in DataArray.sel(self, indexers, method, tolerance, drop, **indexers_kwargs)
   1310 def sel(
   1311     self: T_DataArray,
   1312     indexers: Mapping[Any, Any] = None,
   (...)
   1316     **indexers_kwargs: Any,
   1317 ) -> T_DataArray:
   1318     """Return a new DataArray whose data is given by selecting index
   1319     labels along the specified dimension(s).
   1320 
   (...)
   1418     Dimensions without coordinates: points
   1419     """
-> 1420     ds = self._to_temp_dataset().sel(
   1421         indexers=indexers,
   1422         drop=drop,
   1423         method=method,
   1424         tolerance=tolerance,
...
    197     # see https://github.com/pydata/xarray/issues/5727
--> 198     value = np.asarray(value, dtype=dtype)
    199 return value

TypeError: float() argument must be a string or a real number, not 'slice'

Anything else we need to know?

Maybe related to #6836

Environment