to_netcdf: Unexpected drop of "units" attribute of attached "bounds"

What happened?

When writing a Dataset to netcdf, any DataArrays that are linked as bounds through another variables attrs['bounds'] entry, have their (specifically) 'units' attribute dropped inside the written netcdf file.

See example

What did you expect to happen?

Units attribute to be written to the netcdf file.

Minimal Complete Verifiable Example

import numpy as np
import xarray as xr

# Create a new Dataset
ds = xr.Dataset()

# Add the x variable, Specify 'x_bnds' as bounds, defined later.
ds['x'] = xr.DataArray(np.arange(10), dims='x', attrs={'units':'m', 'bounds':'x_bnds'})

# Bounds require an extra dimension equal to number of vertices.
ds['nv'] = xr.DataArray(np.r_[0, 1], dims='nv')

# Add the actual bounding values for variable x.
ds['x_bnds'] = xr.DataArray(np.squeeze(np.dstack([np.arange(10)-0.5, np.arange(10)+0.5])),  
                            dims=['x', 'nv'],
                            attrs={'test':4, 'units':'m', })

print('Units is attached to the bounds in the dataset before writing', 'units' in ds['x_bnds'].attrs)

# Write to netcdf file
ds.to_netcdf('tmp.nc', format='netcdf4', engine='netcdf4')

# Open the dataset and check x_bnds attrs.  units is dropped.
new = xr.open_dataset('tmp.nc')
print(new['x_bnds'].attrs)

# Confirm that units were never written to the file.
!h5dump -d /x_bnds tmp.nc

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.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

No response

Anything else we need to know?

No response

Environment

Use the issue's minimal example as the first check and trace the Dataset.to_netcdf entry point through the netCDF4 engine. Done means the linked x_bnds DataArray retains its units attribute after writing and reopening the NetCDF file.