Refactor groupby to rely less on storing keys as `Index` objects

[shwina]

#11792 introduces the ability to group on list columns. In the future, we can expect grouping by, e.g., structs and other types that are not supported by Pandas.

In #6932, we made the decision not to support creating an Index with elements of type list.

Unfortunately, our groupby internals rely heavily on being able to store the key columns of a groupby as an Index. In particular, the internal _Grouping.keys method is heavily used.

We should rely less on storing keys as Index objects, which will make it much easier to support grouping by lists and structs.