Heat pump water heaters already exist. These are hybrid things where a traditional electric water heater is fitted with a heat pump. The heat pump can increase the water temp but cannot deliver enough, so heating elements are still needed to reach a usable temp.
I’m wondering if that design can be improved on this way: instead of powering the heat pump from the wall, the heat pump can be connected directly to a PV. I think that would be more efficient and cheaper because PV output is not normally directly usable. IIUC, it’s variable D/C which must be regulated and/or inverted to A/C involving more hardware, conversion, and waste. But exceptionally, I’ve heard that a PV can directly power a compressor with no middleware. Any reasons this would be infeasible or uninteresting?
Of course the tank still needs wall power for the heating elements, but would use less wall power and entail less conversion loss.
There are 'hybrid' heat pump mini splits (for air conditioning / cooling) that take both AC and DC input. (See airspool, EG4, and hotspotenergy)
All of these are configured to have dc compressors and AC to DC inverters.
If you have a hybrid system, you either take the conversion losses on the AC or DC input.
For aircon, having the losses on AC to DC conversion makes the most sense - if it's hot out, it should be bright out and there should be plenty of DC solar output - and topping off with a little AC and taking a loss should be fine.
I don't think this is the case with water heaters on average - if it's cold and cloudy or night you're still going to want hot water. I think it makes sense if you're in the desert - but most people are not going to be. So don't think this will be done commercially