add join argument to xr.broadcast?

Is your feature request related to a problem?

xr.broadcast always does an outer join:

https://github.com/pydata/xarray/blob/de965f342e1c9c5de92ab135fbc4062e21e72453/xarray/core/alignment.py#L702

https://github.com/pydata/xarray/blob/de965f342e1c9c5de92ab135fbc4062e21e72453/xarray/core/alignment.py#L768

This is not how the (default) broadcasting (arithmetic join) works, e.g. the following first does an inner join and then broadcasts:

import xarray as xr

da1 = xr.DataArray([[0, 1, 2]], dims=("y", "x"), coords={"x": [0, 1, 2]})
da2 = xr.DataArray([0, 1, 2, 3, 4], dims="x", coords={"x": [0, 1, 2, 3, 4]})
da1 + da2

<xarray.DataArray (y: 1, x: 3)>
array([[0, 2, 4]])
Coordinates:
  * x        (x) int64 0 1 2
Dimensions without coordinates: y

Describe the solution you'd like

Add a join argument to xr.broadcast. I would propose to leave the default as is

def broadcast(*args, exclude=None, join="outer"):
    args = align(*args, join=join, copy=False, exclude=exclude) 

Describe alternatives you've considered

• We could make broadcast respect options -> arithmetic_join but that would be a breaking change and I am not sure how the deprecation should/ would be handled...
• We could leave it as is.

Additional context

• xr.broadcast should not be used often because this is should happen automatically in most cases
• in #6059 I use broadcast because I couldn't get it to work otherwise (maybe there is a better way?). However, the "outer elements" are immediately discarded again - so it's kind of pointless to do an outer join.

import numpy as np
import xarray as xr

da = xr.DataArray(np.arange(6).reshape(3, 2), coords={"dim_0": [0, 1, 2]})
w = xr.DataArray([1, 1, 1, 1, 1, 1], coords={"dim_0": [0, 1, 2, 4, 5, 6]})
da.weighted(w).quantile(0.5)

Start in xarray/core/alignment.py at the linked xr.broadcast implementation and review how it calls align, including the existing exclude handling. Check the requested join behavior against the arithmetic example and the weighted quantile context. Done means xr.broadcast accepts the proposed join argument while preserving the current outer-join default.