datatree gets dis-aligned in binary op

### What happened?

Subtracting a dataset from a datatree can cause a `ValueError: group '/a' is not aligned with its parents` ~even though the parent dt is valid~ even though the resulting nodes are only siblings.

### What did you expect to happen?

This to work. (I don't yet understand the design decision why the parents have to be aligned. I think together with the nodes that cannot be empty this leads to problems.)

### Minimal Complete Verifiable Example

```Python
import xarray as xr

dt = xr.DataTree()

a = xr.Dataset(data_vars={"x": [10, 20]}, coords={"time": [0, 1]})
b = xr.Dataset(data_vars={"x": [11, 22, 33]}, coords={"time": [0, 1, 2]})

dt["a"] = a
dt["b"] = b

dt - b # fails
```

### MVCE confirmation

- [ ] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [ ] Complete example — the example is self-contained, including all data and the text of any traceback.
- [ ] Verifiable example — the example copy & pastes into an IPython prompt or [Binder notebook](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [ ] New issue — a search of GitHub Issues suggests this is not a duplicate.
- [ ] Recent environment — the issue occurs with the latest version of xarray and its dependencies.

### Relevant log output

```Python
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree.py:149, in check_alignment(path, node_ds, parent_ds, children)
    148 try:
--> 149     align(node_ds, parent_ds, join="exact", copy=False)
    150 except ValueError as e:

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/alignment.py:883, in align(join, copy, indexes, exclude, fill_value, *objects)
    875 aligner = Aligner(
    876     objects,
    877     join=join,
   (...)
    881     fill_value=fill_value,
    882 )
--> 883 aligner.align()
    884 return aligner.results

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/alignment.py:575, in Aligner.align(self)
    574 self.assert_no_index_conflict()
--> 575 self.align_indexes()
    576 self.assert_unindexed_dim_sizes_equal()

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/alignment.py:422, in Aligner.align_indexes(self)
    421 if self.join == "exact":
--> 422     raise ValueError(
    423         "cannot align objects with join='exact' where "
    424         "index/labels/sizes are not equal along "
    425         "these coordinates (dimensions): "
    426         + ", ".join(f"{name!r} {dims!r}" for name, dims in key[0])
    427     )
    428 joiner = self._get_index_joiner(index_cls)

ValueError: cannot align objects with join='exact' where index/labels/sizes are not equal along these coordinates (dimensions): 'x' ('x',)

The above exception was the direct cause of the following exception:

ValueError                                Traceback (most recent call last)
Cell In[18], line 11
      8 dt["a"] = a
      9 dt["b"] = b
---> 11 dt - b # fails

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/_typed_ops.py:40, in DataTreeOpsMixin.__sub__(self, other)
     39 def __sub__(self, other: DtCompatible) -> Self:
---> 40     return self._binary_op(other, operator.sub)

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree.py:1548, in DataTree._binary_op(self, other, f, reflexive, join)
   1540     return NotImplemented
   1542 ds_binop = functools.partial(
   1543     Dataset._binary_op,
   1544     f=f,
   1545     reflexive=reflexive,
   1546     join=join,
   1547 )
-> 1548 return map_over_datasets(ds_binop, self, other)

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree_mapping.py:111, in map_over_datasets(func, *args)
    108 if num_return_values is None:
    109     # one return value
    110     out_data = cast(Mapping[str, Dataset | None], out_data_objects)
--> 111     return DataTree.from_dict(out_data, name=name)
    113 # multiple return values
    114 out_data_tuples = cast(Mapping[str, tuple[Dataset | None, ...]], out_data_objects)

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree.py:1198, in DataTree.from_dict(cls, d, name)
   1196         else:
   1197             raise TypeError(f"invalid values: {data}")
-> 1198         obj._set_item(
   1199             path,
   1200             new_node,
   1201             allow_overwrite=False,
   1202             new_nodes_along_path=True,
   1203         )
   1205 # TODO: figure out why mypy is raising an error here, likely something
   1206 # to do with the return type of Dataset.copy()
   1207 return obj

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/treenode.py:652, in TreeNode._set_item(self, path, item, new_nodes_along_path, allow_overwrite)
    650         raise KeyError(f"Already a node object at path {path}")
    651 else:
--> 652     current_node._set(name, item)

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree.py:944, in DataTree._set(self, key, val)
    942     new_node = val.copy(deep=False)
    943     new_node.name = key
--> 944     new_node._set_parent(new_parent=self, child_name=key)
    945 else:
    946     if not isinstance(val, DataArray | Variable):
    947         # accommodate other types that can be coerced into Variables

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/treenode.py:115, in TreeNode._set_parent(self, new_parent, child_name)
    113 self._check_loop(new_parent)
    114 self._detach(old_parent)
--> 115 self._attach(new_parent, child_name)

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/treenode.py:152, in TreeNode._attach(self, parent, child_name)
    147 if child_name is None:
    148     raise ValueError(
    149         "To directly set parent, child needs a name, but child is unnamed"
    150     )
--> 152 self._pre_attach(parent, child_name)
    153 parentchildren = parent._children
    154 assert not any(
    155     child is self for child in parentchildren
    156 ), "Tree is corrupt."

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree.py:528, in DataTree._pre_attach(self, parent, name)
    526 node_ds = self.to_dataset(inherit=False)
    527 parent_ds = parent._to_dataset_view(rebuild_dims=False, inherit=True)
--> 528 check_alignment(path, node_ds, parent_ds, self.children)
    529 _deduplicate_inherited_coordinates(self, parent)

File ~/.conda/envs/mesmer-tests/lib/python3.13/site-packages/xarray/core/datatree.py:153, in check_alignment(path, node_ds, parent_ds, children)
    151         node_repr = _indented(_without_header(repr(node_ds)))
    152         parent_repr = _indented(dims_and_coords_repr(parent_ds))
--> 153         raise ValueError(
    154             f"group {path!r} is not aligned with its parents:\n"
    155             f"Group:\n{node_repr}\nFrom parents:\n{parent_repr}"
    156         ) from e
    158 if children:
    159     if parent_ds is not None:

ValueError: group '/a' is not aligned with its parents:
Group:
    Dimensions:  (x: 0, time: 2)
    Coordinates:
      * x        (x) int64 0B 
      * time     (time) int64 16B 0 1
    Data variables:
        *empty*
From parents:
    Dimensions:  (x: 3, time: 3)
    Coordinates:
      * x        (x) int64 24B 11 22 33
      * time     (time) int64 24B 0 1 2
```

### Anything else we need to know?

_No response_

### Environment

<details>

INSTALLED VERSIONS
------------------
commit: None
python: 3.13.1 | packaged by conda-forge | (main, Jan 13 2025, 09:53:10) [GCC 13.3.0]
python-bits: 64
OS: Linux
OS-release: 6.8.0-52-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: ('en_US', 'UTF-8')
libhdf5: 1.14.4
libnetcdf: 4.9.2

xarray: 2025.1.2.dev26+gd7ac79a3
pandas: 3.0.0.dev0+1875.gc36da3f6de
numpy: 2.3.0.dev0+git20250128.a1fa8e1
scipy: 1.16.0.dev0+git20250128.1cbdb24
netCDF4: 1.7.2
pydap: None
h5netcdf: None
h5py: None
zarr: None
cftime: 1.6.4
nc_time_axis: 1.3.1.dev218
iris: None
bottleneck: None
dask: 2025.1.0+9.gc08f8e50
distributed: 2025.1.0
matplotlib: 3.11.0.dev400+g71f5cf3a07
cartopy: 0.24.0
seaborn: None
numbagg: None
fsspec: 2024.12.0
cupy: None
pint: None
sparse: None
flox: None
numpy_groupies: None
setuptools: 75.8.0
pip: 25.0
conda: None
pytest: 8.3.4
mypy: None
IPython: 8.31.0
sphinx: None

</details>


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datatree gets dis-aligned in binary op #10013

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Uh oh!

datatree gets dis-aligned in binary op #10013

Description

What happened?

What did you expect to happen?

Minimal Complete Verifiable Example

MVCE confirmation

Relevant log output

Anything else we need to know?

Environment

INSTALLED VERSIONS

Metadata

Metadata

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Labels

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