Are there any thermostats (any type) that are smart enough not to
turn on the heat at 10:55 when they are programmed to set back at
11:00? It seems wasteful and hard on the equipment to do so.

Also for heat pump thermostats, are there any out there that will
not activate stage 2 (electric aux heat) during normal setback
recovery. If it is 45 degrees outside, I don't want the aux heat
immediately coming on every morning just because the thermostat
is set to warm the house to the morning temp setting.