Update group by multi index

ideally GroupBy._infer_concat_args() would return a xr.Coordinates object that contains both the coordinate(s) and their (multi-)index to assign to the result (combined) object.

The goal is to avoid calling create_default_index_implicit(coord) below where coord is a pd.MultiIndex or a single IndexVariable wrapping a multi-index. If coord is a Coordinates object, we could do combined = combined.assign_coords(coord) instead.

https://github.com/pydata/xarray/blob/e2b6f3468ef829b8a83637965d34a164bf3bca78/xarray/core/groupby.py#L1573-L1587

There are actually more general issues:

• The group parameter of Dataset.groupby being a single variable or variable name, it won't be possible to do groupby on a full pandas multi-index once we drop its dimension coordinate (#8143). How can we still support it? Maybe passing a dimension name to group and check that there's only one index for that dimension?
• How can we support custom, multi-coordinate indexes with groupby? I don't have any practical example in mind, but in theory just passing a single coordinate name as group will invalidate the index. Should we drop the index in the result? Or, like suggested above pass a dimension name as group and check the index?

Originally posted by @benbovy in https://github.com/pydata/xarray/issues/8140#issuecomment-1709775666

Start in xarray/core/groupby.py around lines 1573-1587 and inspect GroupBy._infer_concat_args(), especially how MultiIndex and IndexVariable values reach create_default_index_implicit(). Then resolve the broader groupby behavior questions for full pandas multi-indexes and custom multi-coordinate indexes; done means the intended coordinate and index behavior is defined and supported.