https://www.theregister.co.uk/2019/09/20/nest_cant_use_g_suite_emails/

Nest users are shouting at Google to let them register G Suite accounts to their home assistant and automation devices.

We're waiting to hear back from Google, but so far its tech support is sticking to the line that there is no way to register a G Suite account and only a freebie Gmail addy will do.