Variable-compressor fridges will be more thermodynamically efficient, as the heat transfer happens more gradually, so temperature differences across the heat pump will be lower (e.g. because the condenser will have more time to gradually transfer heat to the room, it won't get as hot). And coefficient of performance for a heat pump is higher if the temperature difference is smaller. Another way to achieve this might be with a variable-displacement compressor (which is how modern car AC systems work, rather than cycling on/off).
Unlikely. The thermal timescales are long enough that the fridge turning on and off doesn't mean the temperatures vary wildly. That's why they can do it in the first place!
Central heating on the other hand... I'm definitely never buying a boiler without opentherm.
I think the comment you’re replying to is referring to steady state performance. At lower refrigerant flow, the temperature difference produced by the system will be lower and thus the thermodynamic efficiency will be higher.
(A fridge is producing a temperature difference between the hot gas exiting the compressor and the cold liquid/gas mixture coming out of the expansion valve. The former will be quite a bit hotter than the outside air and the latter will be quite a bit colder than the air inside the fridge. The smaller the value of “quite a bit” the higher the Carnot efficiency would be.)
