Use a normal domestic one, your just heating a buffer as far as it's concerned. Depending on hot tub size a big one. To keep the ASHP inhibited and pressurised you may need to plate load the hot tub, but size the Plate Heat Exchanger (PHE) correctly, you have a 2 Deg approach temp. Then you have no issues with DHW heating, it just switches the diverter valve as normal. Add a second zone for cooling, so it bypasses the hot tub or have the hot tub cooler in summer and as cooling buffer. Heat pump doesn't care if it doing heating or cooling it just moving the refrigerant 4 port valve to a different position (as long manufacturer hasn't disabled the cooling function).
Most heat pumps have the functionality to have different zones as cooling only, heat only or both. And the functions can be independently set for each zone.