DataArray.to_dataset(dim=...) does not preserve attributes

What happened:
When calling DataArray.to_dataset(dim=...) for splitting the array along one dimension, its attributes are copied to the resulting Dataset but not to the variables.

What you expected to happen:
Attributes are copied to the variables.

Minimal Complete Verifiable Example:

import numpy as np
import xarray as xr

# this setting does not change the behaviour
xr.set_options(keep_attrs=True)

data = np.arange(2*3*4, dtype="uint16").reshape((2,3,4))
coords = [("band", ["1", "2"]), ("y", np.arange(3)), ("x", np.arange(4))]
da = xr.DataArray(data, coords=coords, attrs=dict(myattr=9999))
da

# the attribute is always copied to the Dataset regardless of the promote_attrs value
ds_split = da.to_dataset("band", promote_attrs=False)
ds_split

Anything else we need to know?:
If I avoid the splitting, the attribute is only in the Variable and not in the Dataset.

ds_3d = da.to_dataset(name="ds_3d")
ds_3d

This reproduces the expected behaviour:

ds_sel = xr.Dataset({band: da.sel(band=band, drop=True) for band in da.band.values})
ds_sel

Environment:

Start with the DataArray.to_dataset(dim=...) entry point and run the minimal NumPy/xarray example from the issue, comparing the split Dataset variables with the direct selection result. Trace how attrs are handled when splitting along the dimension and add a regression test that verifies variable attributes are preserved.