apply_ufunc + dask="parallelized" + no core dimensions should raise a nicer error about core dimensions being absent

What happened?

From https://github.com/pydata/xarray/discussions/6370

Calling apply_ufunc(..., dask="parallelized") with no core dimensions and dask input "works" but raises an error on compute (ValueError: axes don't match array from np.transpose).

xr.apply_ufunc(
    lambda x: np.mean(x),
    dt,
    dask="parallelized"
)

What did you expect to happen?

With numpy data the apply_ufunc call does raise an error:

xr.apply_ufunc(
    lambda x: np.mean(x),
    dt.compute(),
    dask="parallelized"
)

ValueError: applied function returned data with unexpected number of dimensions. Received 0 dimension(s) but expected 1 dimensions with names: ('x',)

Minimal Complete Verifiable Example

import xarray as xr

dt = xr.Dataset(
    data_vars=dict(
        value=(["x"], [1,1,2,2,2,3,3,3,3,3]), 
    ),
    coords=dict(
        lon=(["x"], np.linspace(0,1,10)),
    ),
).chunk(chunks={'x': tuple([2,3,5])}) # three chunks of different size

xr.apply_ufunc(
    lambda x: np.mean(x),
    dt,
    dask="parallelized"
)

Relevant log output

No response

Anything else we need to know?

No response

Environment

N/A

Start at the apply_ufunc entry point and compare the dask="parallelized" path with the numpy-data behavior shown in the issue. The work is done when inputs with no core dimensions raise a clear ValueError before compute, rather than failing later in np.transpose with "axes don't match array".