How to migrate to "Works with Google Assistant" account in order to use Nest Camera inside Google Nest Hub Max

I’ve just bought a Google Nest Hub Max and I would like to use the camera in it, at least with the Google Home application.
I already have an old Nest developer account and I do have a Nest thermostat integrated in Home Assistant.
If I try to configure the Google Nest Hub Max Camera inside the Google Home application, it asks me to migrate the account to the Google account.

Will this stop to work my Nest integration in Home Assistant?
Is there anyone that has already migrated the account with a Nest thermostat?