This is still a problem on iOS 16.02. I have an iPhone 14 Plus that I've had for 3 days now. I'm using the Google Home app because we (only) have a Nest Camera with Floodlight and a Nest Doorbell (battery). Background app refresh is not turned on. and I have location for the Google Home app set to "while I'm using the app". Just looked at my phone and the Google Home app has used 85% of my battery, really drained that battery down quickly. No notifications from the Nest cameras during the period of time that the Home app was draining my battery.
At this rate, I'll either have to dump the iPhone, or the Nest cameras...this never happened in several months using a Google Pixel 6 phone. I don't have any other home automation going on, no use of HomeKit, no Google Home appliances, just the two Nest cameras.
I also reported this in "Feedback" on the Google Home app, so I'm pursuing all avenues that I can think of. This is really stupendous battery usage by a single app, no reason for it, it's someone's bug. But I'm sure that it will destroy my phone battery before too long if this continues. When I saw the battery drain, and Google Home app owning 85% of it, I immediately uninstalled and re-installed the Google Home App. It has not recurred since then, that was a couple of hours ago.
Has anyone encountered this that has a workaround? I've tried turning off Location for the app now, and will try to remember to exit the app from the main menu only, which should turn off any streaming video. But again, this didn't happen on a Pixel phone over quite a period of time with no need for thinking about how I'm exiting from the app or worrying about Location setting. And occurred within 3 days when I got a new iPhone.