Morning,
I'm chiming in once again. So, 4K is definitely realistic. There is more than enough cooling capacity available, the only problem and thus the reason why "only" 4K below outdoor temperature can be achieved is that the dew point must not be undershot. A more elegant solution would be heating the house using chests, which would then be used both for heating and cooling the house. (Chest --> ventilation unit with heat exchanger and forced ventilation) In these chests, the 10°C supply temperature from the primary circuit of the heat pump could be fully utilized since the condensate formed is directly drained out of the chest and uncontrolled dew point undershooting (condensate formation) does not occur inside the room.
Regarding the effort, any cooling realized with an active cooling unit is and remains an energy guzzler. The expensive split air conditioning units would still be the cheaper alternative, the "cheap" split air conditioning systems without performance control are not even the most expensive option. The mobile units with the exhaust hose are hardly to be outdone, except by an air-water heat pump used for cooling....
Incidentally, even large companies with technical applications use this type of cooling. The only thing that is not optimal is simply the arrangement of the heat exchanger surface in the building. Heat rises upwards, which is why underfloor heating is often used. Actually, the heat exchanger surface for cooling should be installed at the top (there are cooling ceilings for this), whereby the dew point undershooting must be prevented here as well (there are control systems that prevent this). Alternatively, there is also the option to realize heating and cooling by means of ventilation systems (partial air conditioning systems). And the solution with the chests falls into this category. This chest solution is or was successfully used by a large house construction company. This would also be feasible with a ventilation system if you have a heat pump using geothermal energy in operation.