My Nest experience is limited to my 4-1/2 year old Nest Cam Outdoor models. These are WiFi for data but require wired power.
These are old enough that they work with the Nest app. That app allows cameras to be turned on or off on a schedule set in the app. And, as you mentioned, cameras can be turned on or off based on geolocation of your phone(s).
Newer cameras that can only be controlled by the Google Home app cannot be scheduled.
And so far as I know, no Nest cameras can be turned on or off via SmartThings or other external tool.