Quoted from DBLM:

It could just be a terminology thing, but auxiliary heat and emergency heat are not the same thing. Auxiliary heat is a secondary source that augments the heat pump and emergency heat is just the heating strips in case your heat pump goes down. This is a pretty good explanation https://beachairobx.com/heat-pump-auxiliary-heat/
I would ask your hvac guy what your auxiliary heat source is. It sounds like they are talking an electric source. Ask them if you have enough for a gas two stage as goodomens mentions and what I have. This setup works incredibly well.

Quoted from Rdoyle1978:

He definitely said "emergency heat," but described it closer to what you're calling "auxiliary heat". Still, the gas two-stage sounds like the way to go. Thanks very much again - this has cleared up in a few minutes of 'real world' that reading on the internet for a week was not making obvious.

Quoted from DBLM:

Glad I could help! For a frame of reference, my Trane 2 stage heat pump installed was about 9.5 or 10K. At some point, I am going to have to replace my main floor unit and will have to make the decision if I stay on heating oil or go to propane. Propane is more efficient from a BTU perspective, but I already have an oil tank in the house. Will figure it out. Joys of living down the peninsula away from maintained infrastructure.
When this Covid thing dies down we will have to meet up at VUK or MOMS or Lymans. I am normally always around the city. Of course, if you like seafood, you can always come out this way.

Quoted from GoodOmens:

Heatpumps are super-efficient. Granted my electricity rates here are dirt (~$.10 cents a kwh, transmission included), but the highest my bill is during the winter is around $145ish with my gas around $30 to heat around 2400 sqft, and I have a gas stove I use all the time and gas water heater. I also have an electric car that uses about ~$35 of that electricity.