Zarr error when trying to overwrite part of existing store

What happened?

to_zarr threw an error when I tried to overwrite part of an existing zarr store.

What did you expect to happen?

With mode w I was expecting it to overwrite part of the store with no complaints.

I expected that because that's what the docstring of to_zarr says:

mode ({"w", "w-", "a", "r+", None}, optional) – Persistence mode: “w” means create (overwrite if exists); “w-” means create (fail if exists); “a” means override existing variables (create if does not exist);

The default mode is "w", so I was expecting it to overwrite.

Minimal Complete Verifiable Example

import xarray as xr
import numpy as np
np.random.seed(0)

ds = xr.Dataset()
ds["data"] = (['x', 'y'], np.random.random((100,100)))
ds.to_zarr("test.zarr")
print(ds["data"].mean().compute())
# returns array(0.49645889) as expected

ds = xr.open_dataset("test.zarr", engine='zarr', chunks={})
ds["data"].mean().compute()
print(ds["data"].mean().compute())
# still returns array(0.49645889) as expected

ds.to_zarr("test.zarr", mode="a")

<xarray.DataArray 'data' ()>
array(0.49645889)
<xarray.DataArray 'data' ()>
array(0.49645889)
Traceback (most recent call last):
  File "/home/tom/Documents/Work/Code/experimentation/bugs/datatree_nans/mwe_xarray.py", line 16, in <module>
    ds.to_zarr("test.zarr")
  File "/home/tom/miniconda3/envs/xrdev3.9/lib/python3.9/site-packages/xarray/core/dataset.py", line 2091, in to_zarr
    return to_zarr(  # type: ignore
  File "/home/tom/miniconda3/envs/xrdev3.9/lib/python3.9/site-packages/xarray/backends/api.py", line 1628, in to_zarr
    zstore = backends.ZarrStore.open_group(
  File "/home/tom/miniconda3/envs/xrdev3.9/lib/python3.9/site-packages/xarray/backends/zarr.py", line 420, in open_group
    zarr_group = zarr.open_group(store, **open_kwargs)
  File "/home/tom/miniconda3/envs/xrdev3.9/lib/python3.9/site-packages/zarr/hierarchy.py", line 1389, in open_group
    raise ContainsGroupError(path)
zarr.errors.ContainsGroupError: path '' contains a group

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, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.

Relevant log output

No response

Anything else we need to know?

I would like to know what the intended result is supposed to be here, so that I can make sure datatree behaves the same way, see https://github.com/xarray-contrib/datatree/issues/168.

Environment

Main branch of xarray, zarr v2.13.3

Start by running the provided MVCE, then trace mode handling from xarray/core/dataset.py through xarray/backends/api.py and xarray/backends/zarr.py to zarr.open_group. Determine the intended overwrite semantics for an existing store, then ensure the resulting behavior and documentation agree with that decision.