`Dataset.broadcast_like(other)` should broadcast against like variables in other

Is your feature request related to a problem?

I am a bit puzzled about how xarrays is broadcasting Datasets.
It seems to always add all dimensions to all variables.
Is this what you want in general?

See this example:

import xarray as xr

da = xr.DataArray([[1, 2, 3]], dims=("x", "y"))
# <xarray.DataArray (x: 1, y: 3)>
# array([[1, 2, 3]])
ds = xr.Dataset({"a": ("x", [1]), "b": ("z", [2, 3])})
# <xarray.Dataset>
# Dimensions:  (x: 1, z: 2)
# Dimensions without coordinates: x, z
# Data variables:
#     a        (x) int32 1
#     b        (z) int32 2 3
ds.broadcast_like(da)

# returns:
# <xarray.Dataset>
# Dimensions:  (x: 1, y: 3, z: 2)
# Dimensions without coordinates: x, y, z
# Data variables:
#     a        (x, y, z) int32 1 1 1 1 1 1
#     b        (x, y, z) int32 2 3 2 3 2 3

# I think it should return:
# <xarray.Dataset>
# Dimensions:  (x: 1, y: 3, z: 2)
# Dimensions without coordinates: x, y, z
# Data variables:
#     a        (x, y) int32 1 1 1  # notice here without "z" dim
#     b        (x, y, z) int32 2 3 2 3 2 3

Describe the solution you'd like

I would like broadcasting to behave the same way as e.g. a simple addition.
In the upper example da + ds produces the dimensions that I want.

Describe alternatives you've considered

ds + xr.zeros_like(da) this works, but seems more like a "dirty hack".

Additional context

Maybe one can add an option to broadcasting that controls this behavior?

Start at Dataset.broadcast_like and compare its behavior with the DataArray-plus-Dataset example in the issue. Determine whether broadcasting should follow each variable's existing dimensions; done when the example preserves a's lack of z while b includes x, y, and z, with regression coverage for the behavior.