@2kidsdad
The new Google Nest Doorbell (Battery), judging from customer reports, seems to run off the battery, and, when hard-wired, seems to be designed to trickle-charge the battery at a level low enough so that it does not trigger the chime. In addition, the battery seems to be unable to charge very well at lower temperatures.
See this very long thread with over 300 customer replies on the effects of cold weather--with temperatures well within operating temperatures--on the battery doorbell:
https://www.googlenestcommunity.com/t5/Cameras-and-Doorbells/Cold-weather-concerns-with-Nest-Doorbel...
By comparison, the new Google Nest Camera (Battery), when plugged in with the optional power cable (which is what we have), does NOT seem to have the same problems. As long as it's plugged in, it seems to run off of the incoming power. Our camera always shows as "Live" and if we go to Settings | Battery, it says "Plugged in" with an infinity symbol. If we unplug or disconnect the power and click on the camera in the Google Home app, it shows as "Idle" with a battery percentage of 100%, even with Minnesota temperatures ranging down to -18 degrees Fahrenheit. We don't have the battery doorbell, so I don't know how it is supposed to appear in the Google Home app when it is hard-wired and receiving power.
