fix: preserve scalar variables in reduce operations (GH#11417)

[C1-BA-B1-F3]

Problem

When calling Dataset.sum() (or other numeric-only reduce operations like mean, std, etc.) on a dataset with scalar (0-dimensional) non-numeric data variables, it raises:

TypeError: the resolved dtypes are not compatible with add.reduce. Resolved (dtype('<U5'), dtype('<U5'), dtype('<U10'))

Reproduction

import xarray as xr
ds = xr.Dataset(data_vars={
    'a': (['index'], [1, 2, 3]),
    'd': ([], 'hello')
})
ds.sum('index')  # Raises TypeError

Root Cause

In Dataset.reduce(), the reduce_maybe_single logic determines which axis to pass to the reduction function. For a 0-dimensional scalar variable with no matching reduce dimensions:

• reduce_dims = [] (empty)
• len(reduce_dims) == var.ndim → 0 == 0 → True
• var.ndim != 1 → 0 != 1 → True
• reduce_maybe_single = None (reduce over all dims)

This causes var.reduce(func, dim=None) which calls func(self.data) without an axis argument. For string scalars, this fails because numpy's add.reduce can't handle string concatenation.

Fix

Added a check that reduce_dims is non-empty before setting reduce_maybe_single = None. When reduce_dims is empty (variable doesn't have the target dimension), reduce_maybe_single stays as [] (empty list), which triggers the invariant_0d check in duck_array_ops and returns the scalar value unchanged.

reduce_maybe_single = (
    None
    if reduce_dims
    and len(reduce_dims) == var.ndim
    and var.ndim != 1
    else reduce_dims
)

Test

Added test_reduce_string_scalar to verify that:

• sum('index') preserves string scalar variables
• mean('index') preserves string scalar variables
• min('index') preserves string scalar variables
• max('index') preserves string scalar variables

Closes #11417