CF accessor adds grid mapping as coordinate

Start by running the minimal example and tracing the ds.cf[standard_name] accessor alongside Dataset.assign(). Determine whether adding the grid-mapping variable as a coordinate is intended; done should include an agreed behavior for coordinate handling that avoids the shown MergeError, with a regression check for the example.

Possibly a duplicate of #357 or a discussion topic. Opinions welcomed.

Description

Since cf_xarray == 0.8.0 (#391), selecting variables by standard name with ds.cf[standard_name] results in a different set of coordinates than selecting them by their short name with ds[short_name]. This prevents re-injecting these variables in a compatible (and even the original) dataset using Dataset.assign() (and possibly other xarray merge operations). Instead trying to Dataset.assign() a cf-picked, georeferenced variable into a raises a MergeError.

Could you help me to understand if this is a design choice or a bug? In my case it comes as a breaking change and I am not exactly sure how to go about (as a cf-xarray fix or downstream in https://github.com/juseg/hyoga/issues/73). Happy to contribute as I can.

Miminal example

import xarray as xr
import cf_xarray

# make grid-mapped fake data (or use xr.open_dataset)
ds = xr.Dataset({
    'tas': ((), None, {
        'grid_mapping': 'crs',
        'standard_name': 'air_temperature'}),
    'crs': ((), None, {
        'grid_mapping_name': 'latitude_longitude'})})

# ds and ds.cf variables have different coordinates
print('crs' in ds['tas'].coords)  # False
print('crs' in ds.cf['air_temperature'].coords)  # True

# assign a cf-picked variable (only works on cf_xarray < 0.8.0)
ds.assign(new=ds.cf['air_temperature'])  # xarray.core.merge.MergeError

Error message

Traceback (most recent call last):
  File "/home/julien/git/code/hyoga/bugs/cfxr08.py", line 17, in <module>
    ds.assign(new=ds.cf['air_temperature'])  # xarray.core.merge.MergeError
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/site-packages/xarray/core/dataset.py", line 6080, in assign
    data.update(results)
  File "/usr/lib/python3.12/site-packages/xarray/core/dataset.py", line 4946, in update
    merge_result = dataset_update_method(self, other)
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/site-packages/xarray/core/merge.py", line 1104, in dataset_update_method
    return merge_core(
           ^^^^^^^^^^^
  File "/usr/lib/python3.12/site-packages/xarray/core/merge.py", line 772, in merge_core
    raise MergeError(
xarray.core.merge.MergeError: unable to determine if these variables should be coordinates or not in the merged result: {'crs'}