iPhone is findable
When my phone is off and charging iPhone is findable comes on, but it has never done it before and find mine has always been on
iPhone 12, iOS 16
You just updated to iOS16 is the probable reason.
But why turn the phone off? That is for fixing glitches only, and should not be a regular occurrence. All the iphone housekeeping (aka curating) is done overnight when the phone is on charge, in WiFi and locked, but not powered off.