I know I paid about 1000EUR for an air-air heat-pump with install in Sweden, but that was a decade ago and they cost 1500-2000EUR total these days. I also have a fancy big ground-source heat-pump bigger than most residential ones and that cost under 10000EUR total. So not sure what makes them so expensive in other countries; you'd hope competition kept prices competitive.
In Germany you have very strict laws for construction of water heating. For example the need to install thermostat on any heater even for floor heating. But this implies a lot of complexity for the heat pump installation. Cheap DIY community basically removes all the thermostats and soley controls heating through water temp and flow control to the radiators.
