id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1318369110,I_kwDOAMm_X85OlLdW,6828,xarray.DataArray.str.cat() doesn't work on chunked data,34276374,open,0,,,3,2022-07-26T14:58:16Z,2023-01-17T18:36:14Z,,NONE,,,,"### What happened?

I was trying to concatenate some DataArrays of strings, and it kept just returning the first DataArray without any changes.

### What did you expect to happen?

I was expecting it to just provide the strings, concatenated together with the spearator between them.

### Minimal Complete Verifiable Example

```Python
da = xr.DataArray(
    np.zeros((2, 2)).astype(str),
    coords={'x':np.arange(2), 'y': np.arange(2)},
    dims=['x', 'y'])

dac = da.chunk()

print((da == dac).values.all())
print((da.str.cat(da, sep='--') == dac.str.cat(dac, sep='--')).values.all())
print((da.str.cat(da, sep='--') == dac.compute().str.cat(dac.compute(), sep='--')).values.all())

>>> True
>>> False
>>> True
```


### MVCE confirmation

- [x] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [x] Complete example — the example is self-contained, including all data and the text of any traceback.
- [x] 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.
- [x] New issue — a search of GitHub Issues suggests this is not a duplicate.

### Relevant log output

_No response_

### Anything else we need to know?

_No response_

### Environment

<details>


INSTALLED VERSIONS
------------------
commit: None
python: 3.8.10 (default, Mar 15 2022, 12:22:08) 
[GCC 9.4.0]
python-bits: 64
OS: Linux
OS-release: 5.11.0-27-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: C.UTF-8
LOCALE: ('en_US', 'UTF-8')
libhdf5: 1.12.2
libnetcdf: 4.9.0

xarray: 2022.3.0
pandas: 1.4.2
numpy: 1.22.4
scipy: 1.8.1
netCDF4: 1.6.0
pydap: None
h5netcdf: 1.0.1
h5py: 3.6.0
Nio: None
zarr: 2.11.3
cftime: 1.6.1
nc_time_axis: None
PseudoNetCDF: None
rasterio: 1.2.10
cfgrib: None
iris: None
bottleneck: None
dask: 2022.7.0
distributed: None
matplotlib: 3.5.2
cartopy: None
seaborn: None
numbagg: None
fsspec: 2022.5.0
cupy: None
pint: None
sparse: None
setuptools: 62.3.2
pip: 22.1.2
conda: None
pytest: None
IPython: 8.3.0
sphinx: None


</details>
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