Does this require a subscription to the Home Asisstant Cloud (NABA CASA) for it to work properly? If so, I think that should be explicitly stated in the documentation.
Unfortunately the Google Nest process is complicated and the slightest mistake prevents it from installing.
One issue I had was that an authentication had remained in HA from a previous installation, even from an attempted installation. Go to:
Settings
Devices and Services
Top right, 3 bullets
Application credentials
Remove the Google Nest authentication and restart the installation process.