I'd probably have gas heat to supplement the heat pump if I didn't have solar and battery to power the home through most nights. And the heat pump water heater giving me free cold air (see post 11) that I put into an air receiver for my home during the warm half of the year, is efficient in part because my HVAC is a variable speed heat pump with var speed air handler. In other words, my HVAC is almost always running, even if at low speed. So just about any time of day that my water heater gives me free cold air, my HVAC is running to draw in the free cold air to spread through the house (so that my home heat pump can be in low speed a few more hours of the day and not have to work as hard making cold air for the home).
Where do you draw air from for your heat pump water heater? Mine has a duct to draw air from the attic (usually warm air, or even really hot air in my Alabama attic). Thus, my water heater heat pump doesn't have to run as long to find enough heat energy to heat the tank. So the attic often has free heat energy that's used to help heat the water tank, and the water heater give me free cold air that I use to help cool the house. The water heater is efficient, and the HVAC is efficient, but the two work together better than the sum of their parts.
I no longer live in the house and had to replace the heat pump after only 10 years. It was a 100% well water system. The primary heat exchanger was well water to Freon. It corroded, leaking water into the Freon. and was no longer available for replacement since the company went bankrupt.
While it worked, it was great. The AC was best. It had a water to air heat exchanger. It primarily used only well water, which was 52 degrees (here in southern Michigan). The system had a feature where it could run the heat pump and use even colder water if the AC cooling was inadequate. It would then dump the heated water into the hot water tank and then out the discharge when that was up to temperature. I never even turned on that feature since the well water air conditioning was quite adequate.
I kept the well water heat exchanger for cooling when the Freon system failed, and it is still doing all the air conditioning in the house some 35 years later.
I had used an ordinary electric water heater tank as a storage tank for the hot water. When the Freon system system failed, I installed a gas furnace for heating, and hooked up electric power to the hot water tank for hot water.