Save groupby codes after factorizing, pass to flox

[dcherian]

• Closes Refactor GroupBy init to avoid factorization #6689,
• xref Update GroupBy constructor for grouping by multiple variables, dask arrays #6610
• Closes groupby_bins groups not correctly applied with built-in methods #7601
• Tests added

This is an alternative to #6689.

• There I tried to avoid factorizing in the GroupBy constructor, and passed the by variable directly to flox. Most GroupBy methods however depend on various steps in __init__, so it became messy.
• Here I instead preserve factorizing in the constructor and pass the factorized codes to flox. This simplifies things a lot. Since we'll want to preserve the "for loop over groups" approach for GroupBy.map, we'll need something like this anyway.

The large amount of deleted code in _flox_reduce here suggests to me that this is the better approach.

I think we could also use this to generalize to multiple groupers:

• factorize each,
• ravel_muti_index to generate a singe variable to groupby
• apply
• reshape to output shape
• assign new indices.

[dcherian]

Just refactored with no functionality changes except to return codes

[dcherian]

I'd like to merge this soon. It's mostly a refactor moving code around, and a major improvement to the flox code path.

Let me know if it'd be easier to split it in to two PRs

[Illviljan]

Hmm, did I mess something up? I believe I only changed typing related things.

_bins suffix seems to have disappeared:

     def test_groupby_bins_multidim(self):
        array = self.make_groupby_multidim_example_array()
        bins = [0, 15, 20]
        bin_coords = pd.cut(array["lat"].values.flat, bins).categories
        expected = DataArray([16, 40], dims="lat_bins", coords={"lat_bins": bin_coords})
        actual = array.groupby_bins("lat", bins).map(lambda x: x.sum())
>       assert_identical(expected, actual)
E       AssertionError: Left and right DataArray objects are not identical
E       Differing dimensions:
E           (lat_bins: 2) != (lat: 2)
E       Coordinates only on the left object:
E         * lat_bins  (lat_bins) object (0, 15] (15, 20]
E       Coordinates only on the right object:
E         * lat       (lat) object (0, 15] (15, 20]

[Illviljan]

Thanks, @dcherian. This LGTM. :)