Google assistant default thermostat

This might be a google assistant question but it’s also HA related in that it’s a generic thermostat entity.

I have a nest thermostat part of Google Home, and have created a generic thermostat in HA (climate.nursery) and have exposed that to google assistant so it also shows up in Home. The issue now is when I say “google turn thermostat on/off” it controls the nursery not the nest in the hallway. Both devices are in their respective “rooms” and no matter what room i’m in when i say it, it uses the nursery. Curious if anyone knows how to re-prioritize thermostats exposed to Google.