I just bought the Nest protect and I too thought I'd be able to learn them into my Google Home app like everything else. Disappointed Google sells this like any of their other devices but doesn't make it clear you have to have a standalone app to run it, I found that how whilst I was installing it.
Been a long time Nest user. Started with thermostat, went to door bell camera, then replaced smoke/CO2 alarms. Same thing happened to me with the Nest Battery Cam. I like the Nest App look and feel much more than the clunky Google Home and prefer to use the Nest App. All devices in on place.
Google provides very poor, and misleading information, they do not make it clear about the app separation they have done.
I have the Nest Protect Smoke and CO2 as well, and I can't add them to Google Home. Stuck using two different apps maintained and owned by one company. Poor customer support