Sorry to post a response even futher off topic, but.... While I was advocating an insulating water heater blanket above, with a heat pump water heater it's a little more complicated. The heat pump section sits atop the water tank, and most configs simply extend the diameter of the tank cladding with the heat pump housing, resulting in a taller cylinder. The heat pump accesses the heat sink thru openings in the housing.
So, commercially available preformed insulation blankets won't work unless made specifically for that heater, facilitating air movement thru the blanket. Perhaps, like cell phone covers, model specific blanket are available? A DIY blanket would have to allow this as well, of course. And ideally, the insulation should be between the tank section and the heat pump section anyhow. Due to the higher efficiency of the unit, all in a quest for diminishing returns perhaps? There are also a couple of other considerations about heat pump water heaters that might be pluses or minuses for certain locations, like they cool and dehumidify the space around them. Therefore they need a condensate drain, and maybe a little pump if no handy gravity solution is available. A plus for me, as it eliminates the need for running a power hog of a dehumidifier in my basement during some seasons, and the pump was easily enough fitted. And in unconditioned spaces, will the heat sink contain sufficient heat for operation in colder seasons? Hybrid mode fixes that, but increases power consumption when your solar production is low.
Do your homework, I guess. Most on these forums seem to be the type that would....