No way to specify compat behaviour for xr.apply_ufunc and ops that use it; binary arithmetic ufuncs don't use arithmetic_compat.

Is your feature request related to a problem?

We're now able to override the problematic (see https://github.com/pydata/xarray/issues/9481, https://github.com/pydata/xarray/issues/10924) compat='minimal' default for arithmetic using e.g. xr.set_options(arithmetic_compat='override'):

import xarray as xr
a = xr.DataArray(1, coords={'foo': 1})
b = xr.DataArray(1, coords={'foo': 2})

with xr.set_options(arithmetic_compat='override'):
     print(a + b)

<xarray.DataArray ()> Size: 8B
array(2)
Coordinates:
    foo      int64 8B 1

Unfortunately there's no way to set compat for xr.apply_ufunc, or for any of the multi-argument ufuncs based on it which perform compat checks

with xr.set_options(arithmetic_compat='override'):
     print(xr.apply_ufunc(lambda x, y: x+y, a, b))

<xarray.DataArray ()> Size: 8B
array(2)

with xr.set_options(arithmetic_compat='override'):
     print(xr.where(True, a, b))

<xarray.DataArray ()> Size: 8B
array(1)

with xr.set_options(arithmetic_compat='override'):
     print(xr.ufuncs.add(a, b))

<xarray.DataArray ()> Size: 8B
array(1)

This is particularly problematic because the behavior now differs for arithmetic operators (going via _binary_op) and arithmetic ufuncs like xr.ufuncs.add or np.add, which go via apply_ufunc.

Describe the solution you'd like / alternatives you've considered

Any views on these options:

(A) : Add an explicit compat argument to apply_ufunc, defaulting to the current behaviour of 'minimal', and let multi-argument ufuncs pass this argument on. (xr.ufuncs based on _binary_ufunc already pass through extra kwargs, but some like xr.dot, xr.where, da.where, da.fillna would need updating.)

(B): Make it configurable via xr.set_options. It could share the existing arithmetic_compat setting which defaults to minimal, or add a new ufunc_compat setting.

(C): (A)+(B): there's an explicit argument for it but it defaults to e.g. OPTIONS["ufunc_compat"]

In all cases I'd suggest setting the defaults to change in a future version to 'override', along with the other planned compat default changes.

If we used the arithmetic_compat setting for apply_ufunc, it'd be reasonable to ask why not for consistency also use arithmetic_join as the default for apply_ufunc's join. However its default is currently different (exact for apply_ufunc, inner for arithmetic), so maybe using a separate ufunc_compat side-steps this.

Start with xr.apply_ufunc and the multi-argument ufunc paths described in the issue, including _binary_ufunc, xr.dot, xr.where, da.where, and da.fillna. Compare how compat is currently selected with arithmetic operators and identify the affected tests or callers. Done means the chosen explicit or option-based compat behavior is applied consistently without changing unrelated defaults.