Inconsistent and unexpected results when grouping by more than one coordinate

What happened?

Grouping by more than one coordinate uses all combinations of coordinates.

What did you expect to happen?

I would expect only the observed combinations to be used.

Minimal Complete Verifiable Example

# /// script
# requires-python = ">=3.11"
# dependencies = [
#   "xarray[complete]@git+https://github.com/pydata/xarray.git@main",
# ]
# ///
#
# This script automatically imports the development branch of xarray to check for issues.
# Please delete this header if you have _not_ tested this script with `uv run`!

import xarray as xr
xr.show_versions()
import numpy as np
import pandas as pd


df = pd.DataFrame(data=dict(test1=[1, 2, 3, 4, 5], test2=[1, 1, 1, 2, 2]))
df['test3'] = df[['test1', 'test2']].apply(tuple, axis=1)
coords = {}
for c in df.columns:
    coords[c] = ("y", df[c].values)
d = xr.DataArray(np.ones((5, 5)), dims=("y", "x"), coords=coords)
d.groupby(["test1", "test2"]).mean()  # generate all combinations of test1 and test2
d.groupby("test3").mean()  # works as expected
# NotImplementedError
# d.set_xindex(["test1", "test2"], PandasMultiIndex).groupby(["test1", "test2"]).mean()

Steps to reproduce

No response

MVCE confirmation

• Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• Complete example — the example is self-contained, including all data and the text of any traceback.
• Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

Anything else we need to know?

No response

Environment

Start by running the supplied MVCE and compare groupby(["test1", "test2"]) with the working tuple-coordinate case. Trace the groupby entry point and its handling of multiple coordinates; done means grouping uses only observed coordinate combinations and the behavior is covered by a regression test.