assign_coords' behavior depends on input DataArrays

What happened?

I'm trying to compute masks (from DataArray's data itself) and assign them as coordinates, but it appears that depending on the combination of coords/dims of the computed masks, sometimes .assign_coords will fail.

It seems like

• it fails when all the mask DataArray's (each is a mask computed, but it probably doesn't matter) to be assigned as coordinates, share a dimension common to the target DataArray, and the dimension contains only a singular value (across all mask DataArray's)
• it doesn't fail when the shared dimension contains more than one value.

It's a bit hard to describe as I don't know the xarray internal itself, but my self-contained minimal example below should demonstrate the issue much clearer.

What did you expect to happen?

No response

Minimal Complete Verifiable Example

import xarray as xr

data = xr.DataArray(
    data=[
        [0, 1, 2], 
        [0, 1, 2]
    ], 
    coords={
        'd1': ['m', 'n'], 
        'd2': ['a', 'b', 'c']
    }
)


# this will fail:
data.assign_coords({'mask_d1_m': data.sel(d1='m')==0})
# ValueError: dimension 'd1' already exists as a scalar variable

# this will fail too:
data.assign_coords({'mask_d1_n': data.sel(d1='n')==0})
# ValueError: dimension 'd1' already exists as a scalar variable

# but this will work:
data.assign_coords(
    {
        'mask_d1_m': data.sel(d1='m')==0,
        'mask_d1_n': data.sel(d1='n')==0
    }
)
# <xarray.DataArray (d1: 2, d2: 3)>
# array([[0, 1, 2],
#        [0, 1, 2]])
# Coordinates:
#   * d1         (d1) <U1 'm' 'n'
#   * d2         (d2) <U1 'a' 'b' 'c'
#     mask_d1_m  (d2) bool True False False
#     mask_d1_n  (d2) bool True False False

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

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[27], line 1
----> 1 data.assign_coords({'mask_d1_n': data.sel(d1='n')==0})

File ~/mambaforge/envs/quickquant/lib/python3.8/site-packages/xarray/core/common.py:615, in DataWithCoords.assign_coords(self, coords, **coords_kwargs)
    613 data = self.copy(deep=False)
    614 results: dict[Hashable, Any] = self._calc_assign_results(coords_combined)
--> 615 data.coords.update(results)
    616 return data

File ~/mambaforge/envs/quickquant/lib/python3.8/site-packages/xarray/core/coordinates.py:177, in Coordinates.update(self, other)
    173 self._maybe_drop_multiindex_coords(set(other_vars))
    174 coords, indexes = merge_coords(
    175     [self.variables, other_vars], priority_arg=1, indexes=self.xindexes
    176 )
--> 177 self._update_coords(coords, indexes)

File ~/mambaforge/envs/quickquant/lib/python3.8/site-packages/xarray/core/coordinates.py:393, in DataArrayCoordinates._update_coords(self, coords, indexes)
    391 coords_plus_data = coords.copy()
    392 coords_plus_data[_THIS_ARRAY] = self._data.variable
--> 393 dims = calculate_dimensions(coords_plus_data)
    394 if not set(dims) <= set(self.dims):
    395     raise ValueError(
    396         "cannot add coordinates with new dimensions to a DataArray"
    397     )

File ~/mambaforge/envs/quickquant/lib/python3.8/site-packages/xarray/core/variable.py:3209, in calculate_dimensions(variables)
   3207 for dim, size in zip(var.dims, var.shape):
   3208     if dim in scalar_vars:
-> 3209         raise ValueError(
   3210             f"dimension {dim!r} already exists as a scalar variable"
   3211         )
   3212     if dim not in dims:
   3213         dims[dim] = size

ValueError: dimension 'd1' already exists as a scalar variable

Anything else we need to know?

No response

Environment

Start by running the minimal example against the current xarray behavior. Trace assign_coords from xarray/core/common.py through xarray/core/coordinates.py and calculate_dimensions in xarray/core/variable.py, then inspect relevant tests around coordinate updates. Done means the demonstrated single-coordinate assignments have defined, consistent behavior without regressing the multi-coordinate case.