to_netcdf / open_dataset is not idempotent

What happened:
I created a Dataset from a Dataarray with a data name equal to its dimension name and no coordinate. When saving the Dataset as netcdf and opening that netcdf as a Dataset again the opened Dataset does not have any data variable and the actual variable has become a coordinate.

What you expected to happen:
I would expect the to_netcdf / open_dataset process to be idempotent and obtain a Dataset that is identical to the one I saved as netcdf.

Minimal Complete Verifiable Example:

import xarray as xr

da = xr.DataArray(
    [1, 2, 3, 4],
    dims=['lat'],
    name='lat'
)
ds = da.to_dataset()

ds.to_netcdf('bug.nc')
ds2 = xr.open_dataset('bug.nc')

print(ds)
print(ds2)

Output

<xarray.Dataset>
Dimensions:  (lat: 4)
Dimensions without coordinates: lat
Data variables:
    lat      (lat) int64 1 2 3 4

<xarray.Dataset>
Dimensions:  (lat: 4)
Coordinates:
  * lat      (lat) int64 1 2 3 4
Data variables:
    *empty*

Anything else we need to know?:

Environment:

Start by running the self-contained example in the issue and compare the printed datasets before and after the to_netcdf/open_dataset round trip. Trace the relevant serialization and loading paths, then verify that the saved data variable remains a data variable and the reopened Dataset matches the original.