DataArrayRolling.mean() ignores `skipna=True` kwarg

What happened?

In the following example, it appears that the skipna=True argument is being ignored, unless you call construct before taking the mean.

What did you expect to happen?

I expected:

da.rolling(time=3).mean("time", skipna=True) == da.rolling(time=3).construct("window").mean("window", skipna=True)

Minimal Complete Verifiable Example

import xarray as xr
import numpy as np

da = xr.DataArray([0, 1, 2, np.NAN, 4, 5, 6], dims="time")

# Results 1 and 2 produce the same array, without skipping NANs
result1 = da.rolling(time=3).mean("time", skipna=True)
result2 = da.rolling(time=3).mean("time", skipna=False)

# Results 3 and 4 produce the expected (different) arrays
result3 = da.rolling(time=3).construct("window").mean("window", skipna=True)
result4 = da.rolling(time=3).construct("window").mean("window", skipna=False)

print(result1)
print(result2)
print(result3)
print(result4)

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.

Relevant log output

<xarray.DataArray (time: 7)>
array([nan, nan,  1., nan, nan, nan,  5.])
Dimensions without coordinates: time
<xarray.DataArray (time: 7)>
array([nan, nan,  1., nan, nan, nan,  5.])
Dimensions without coordinates: time
<xarray.DataArray (time: 7)>
array([0. , 0.5, 1. , 1.5, 3. , 4.5, 5. ])
Dimensions without coordinates: time
<xarray.DataArray (time: 7)>
array([nan, nan,  1., nan, nan, nan,  5.])
Dimensions without coordinates: time

Anything else we need to know?

Note: the first two NaNs are expected due to the min_periods argument to rolling(), but the middle NaNs are what are unexpected when skipna = True

Environment

Start by running the minimal Python example against DataArrayRolling.mean() and compare it with rolling(...).construct("window").mean(...). Check the DataArrayRolling.mean entry point and add coverage for skipna=True versus skipna=False, ensuring the rolling result matches the constructed-window result for the shown NaN input.