My fire alarms went off when I had a power failure.
Only when I opened the Nest app did I see the little red icon in the top left corner (3 bars area) indicating a notification. I clicked on it and there were the notifications of a power failure.
If this had been a fire, well I would have missed it. Nullifying the whole point of buying smart fire alarms.
I have notifications completely turned on in my settings. I use an iPhone 13, iOS 15.4.1. notifications are turned on in the Nest app as well.
I am experiencing this issue also. We have had two power outages and no Notifications were posted on our iPhones. Notifications for Nest Thermostat and Protect are enabled. The only message related to the power outage is posted in the Nest app. In my opinion this is a design deficiency that should be reconciled by Google!