DataTree consolidation to use general AttrAccessMixin class (instead of TreeAttrAccessMixin)

What is your issue?

In #9011 code from datatree was merged into the main xarray/core subdirectory. This includes the TreeAttrAccessMixin class, which is inherited by DataTree. There is also a more general AttrAccessMixin class, which would be preferable to use instead.

The reason that AttrAccessMixin is not just used for DataTree is that AttrAccessMixin.__init_subclass__ has a check to see if there is a __dict__ attribute on the class. If there is, an error is thrown, saying that __slots__ should be used instead. DataTree (and TreeNode and NamedNode) do define __slots__, but there are some attributes that are also declared dynamically (e.g., DataTree.children and DataTree.parent, which are first defined in DataTree.__init__). Because of these dynamic declarations, DataTree has both __slots__ and __dict__ and therefore fails the check in AttrAccessMixin.__init_subcass__.

This issue aims to update DataTree (and potentially NamedNode and TreeNode, if needed), such that DataTree can pass the check in AttrAccessMixin.__init_subclass__ and the additional TreeAttrAccessMixin class can be removed.

Start in xarray/core by reading AttrAccessMixin, TreeAttrAccessMixin, and the DataTree, TreeNode, and NamedNode definitions. Check how slots and dynamic attributes create dict, then verify that DataTree passes AttrAccessMixin.init_subclass; done means TreeAttrAccessMixin can be removed and the relevant classes use the general mixin.