Auto mode on or off probably doesn't make much difference. Auto just controls fan speed, controls which register the air comes out of (floor, face, both, etc) and recirculation mode. Make a change to any one of these and Auto automatically shuts off.
Actually in theory a higher fan speed would be most efficient because then you are getting the maximum amount of heat from the heater coils or cold air from the evaporator coils. But most people don't like air blowing on them so the Auto system will start out with higher fan speed until the cabin heats up (or cools down) then it lowers the fan speed to the minimum that will maintain the set temperature.
What makes a much bigger difference is to use the seat heater in winter as that runs on the 12V system and does not use very much electricity. But even being low powered it is pretty effective because it warms just you not the entire cabin. Whereas cabin heat comes from the high voltage resistance heater located in the engine compartment which heats coolant that gets circulated into the cabin via the normal heater hoses. In milder weather you can often get by with just the seat heater. And in colder weather by using the seat heater you can usually be comfortable with a lower cabin temperature, thus using less resistance heat. Unfortunately in HV mode the car seems to almost never use engine heat from what we can tell, except in extremely cold weather when the resistance heater is not sufficient.
A/C usage doesn't affect mileage as much as the resistance heater, so during summer just use as much A/C as needed to be comfortable. In milder weather you can turn on just the fan, but unfortunately the method to do this is clunky. Just turning off Auto doesn't turn off the A/C compressor. The only way to turn off the A/C compressor is to go into the climate screen, then press the A/C Off button so that Off is highlighted. If neither the A/C On or Off buttons are highlighted then A/C is on. In other words if the A/C On button is highlighted, or if neither the A/C On or Off buttons are highlighted, it's the exact same thing. I don't know if that is the stupidest thing in the Clarity but it's for sure in the top ten.