Refactor Dataset internals to store data variables and coordinate variables as separate dicts

[TomNicholas]

There's a lot of other discussion in #9063, but I wanted to pull out this suggestion for independent discussion:

• Our list of internal attributes on a DataTree node is still not just those on a Dataset plus the inherited coordinates

This is indeed a bit of a con, but in my mind the right fix is probably to adjust the Dataset data model to using dictionaries of data_variables and coord_variables, rather than the current solution of a dict of variables and a set of coord_names. Using a separate dictionary for coord_variables would also be more aligned with how DataArray is implemented. The internal Dataset data model is a hold-over from the very early days of Xarray, before we had a notion of coordinate variables that are not indexes.

Originally posted by @shoyer in #9063 (comment)

[TomNicholas]

In fact could the coord_variables dict just be an actual xr.Coordinates object?

(idea from #9204 (comment))

[shoyer]

In fact could the coord_variables dict just be an actual xr.Coordinates object?

I think Coordinates should remain a thin wrapper object. It needs access to both coordinate Variable objects and associated indexes.

[headtr1ck]

I was wondering about that already quite some time, haha.

Does this mean that handling of coordinates can be handled in the parent class DataWithCoords?

[TomNicholas]

Does this mean that handling of coordinates can be handled in the parent class DataWithCoords?

You mean have all of Dataset, DataArray, and DataTree inherit from DataWithCoords, and add things like the .coords property to DataWithCoords? Relates to #9204 (comment).