We've had a Google Nest Camera (Battery) for 15 months, plugged in with the optional power cable, and it is "Live" all the time and under Settings | Battery shows as "Plugged in" with an infinity symbol.
Is your power cord plugged in securely with the cord feeding towards the FRONT of the camera, as it should? Some customers have reported getting theirs to charge after reseating the USB plug in the bottom of the camera; the plug seems a bit flimsy. Some have reported that the 3-meter charging cord that comes with the camera is defective.
There is no setting in the app to turn charging on or off. I've even seen one post where one customer reported their 10-meter power cable was faulty. And another reported their USB plug fell apart.
I’m sorry for the delay. Let’s sort this out — a few questions: do you have a wired or a wireless setup? Are you able to view the camera feed? Did you receive any notification from the Google Home app? Are your cameras fully charged when you plug it in? Also, has there been a power outage recently?
I appreciate the help, MplsCustomer and Brad.