apply_ufunc should preemptively broadcast

Code Sample

I am having some troubles understanding apply_ufunc broadcasting rules. As I had some trouble understanding the docs, I am not 100% sure it is a bug, but I am quite sure. I will try to explain why with the following really simple example.

import xarray as xr
import numpy as np

a = xr.DataArray(data=np.random.normal(size=(7, 3)), dims=["dim1", "dim2"])
c = xr.DataArray(data=np.random.normal(size=(5, 6)), dims=["dim3", "dim4"])

def func(x,y):
    print(x.shape)
    print(y.shape)
    return

The function defined always raises an error when trying to call apply_ufunc, but this is intended, as the shapes have already been printed by then, and this keeps the example as simple as possible.

Problem description

xr.apply_ufunc(func, a, c)
# Out
# (7, 3, 1, 1)
# (5, 6)

Here, a has been kind of broadcasted, but I would expect the shapes of a and c to be the same as when calling xr.broadcast, as there are no input core dims, so all dimensions are broadcasted. However:

print([ary.shape for ary in xr.broadcast(a,c)])
# [(7, 3, 5, 6), (7, 3, 5, 6)]

Using different input core dims does not get rid of the problem, instead I believe it shows some more issues:

xr.apply_ufunc(func, a, c, input_core_dims=[["dim1"],[]])
# (3, 1, 1, 7), expected (3, 5, 6, 7)
# (5, 6), expected (3, 5, 6)

xr.apply_ufunc(func, a, c, input_core_dims=[[],["dim3"]])
# (7, 3, 1), expected (7, 3, 6)
# (6, 5), expected (7, 3, 6, 5)

xr.apply_ufunc(func, a, c, input_core_dims=[["dim1"],["dim3"]])
# (3, 1, 7), expected (3, 6, 7)
# (6, 5), expected (3, 6, 5)

Is this current behaviour what should be expected?

Output of xr.show_versions()

Start at the xr.apply_ufunc entry point and reproduce the provided examples with the listed inputs, comparing them with xr.broadcast. Trace how input_core_dims and broadcast dimensions are prepared, then determine the intended behavior from the issue's expected shapes. Done means the broadcasting behavior is corrected or clarified and the examples have regression coverage.