'drop_duplicates' behaves differently when using 1 vs many coordinates for an index

What happened?

I am trying to drop_duplicates from a DataArray based on the values of some of the coordinates,
starting from a DataArray with coordinates, but no indexes.

To accomplish this, I call 'DataArray.set_xindex' with the appropriate coordinate names,
and then call 'drop_duplicates' on the resulting DataArray, like so:
 

from xarray import DataArray
import numpy as np

test_array = DataArray(
    np.random.rand(5), 
    coords=dict(x=("sample", [1, 2, 1, 2, 1]), y=("sample", [-1] * 5)),
    dims="sample",
)

# output DataArray's 'sample' dimension has length 2, as expected
good = test_array.set_xindex(["x", "y"]).drop_duplicates("sample")
assert len(good) == 2

The above functions as expected; 'good' has had its duplicates dropped,
and we are left with a DataArray of length 2.

However, the following does not function as I would expect:

# All the 'y's are '-1', so we expect the same duplicates as before to be dropped,
# even if we don't include the 'y' values in the index.
bad = test_array.set_xindex("x").drop_duplicates("sample")
# But this assert fails! 'drop_duplicates' does not drop anything
assert not bad.equals(test_array)

What did you expect to happen?

I expected drop_duplicates to drop the duplicates when I was using only a single coordinate for the index.

Minimal Complete Verifiable Example

from xarray import DataArray
import numpy as np

test_array = DataArray(
    range(5), 
    coords=dict(x=("sample", [1, 2, 1, 2, 1]), y=("sample", [-1] * 5)),
    dims="sample",
)

# output DataArray's 'sample' dimension has length 2, as expected
good = test_array.set_xindex(["x", "y"]).drop_duplicates("sample")
# And indeed there are only 2 elements left after dropping duplicates.
assert len(good) == 2

# All the 'y's are '-1', so we expect the same duplicates as before to be dropped,
bad = test_array.drop_vars("y").set_xindex("x").drop_duplicates("sample")
# But this assert fails! 'drop_duplicates' does not drop anything
assert not bad.equals(test_array.drop_vars("y"))

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

No response

Anything else we need to know?

No response

Environment

Reproduce the provided minimal example first, then trace the DataArray.set_xindex and drop_duplicates entry points to compare single-coordinate and multi-coordinate indexes. Done means a single-coordinate index removes the duplicate samples in the same case where the combined x and y index does.