What is your issue?

I would expect xr.testing.assert_identical to be true if the objects are identical, values, coords, attrs, and indexes. However, it does not test for what coords have an index attached to them. e.g i would expect this to fail, but it does not:

import xarray as xr

ds = xr.Dataset(
    {"data": ("time", [0, 1, 2, 3])},
    coords={"time": [0.1, 0.2, 0.3, 0.4], "time_metadata": ("time", [10, 15, 20, 25])},
)
ds_extra_index = ds.set_xindex("time_metadata")

xr.testing.assert_identical(ds, ds_extra_index)

I would contend that identical includes what has an index. But curious what others think