The task of the heating system in the house is to compensate for the heat losses of the house at an indoor temperature X and an outdoor temperature Y. Therefore, the heating system only needs to supply as much heat as the house loses to the environment. If the house were perfectly insulated (U-value: 0.0) and hermetically sealed, the heating would not need to supply any heat to maintain, for example, 21 degrees inside the house.
The heat loss of the house is calculated from the insulation quality of the building envelope and the temperature difference between inside and outside. The topic of heat loss through ventilation would also be added, but we will leave that aside here.
By lowering the temperature at night, the indoor temperature is reduced, thereby reducing the temperature difference to the outside air and less heat is lost that the heating system needs to replace.
The statement that "heating up" a house consumes more energy than maintaining a certain temperature is not correct. The heat stored in the house is not lost; it is only stored there. Only the losses to the environment are decisive, and these decrease with the temperature difference.
In the case of underfloor heating, the energy savings are virtually zero because the heating system reacts so sluggishly that it simply "smooths out" switching off for a few hours. Of course, this presupposes a certain insulation standard.
With a heat pump, there is an additional factor, namely the strong increase in heating output in the morning, which causes less efficient operation than if it had run at a constant output.
This would only make sense from the perspective that, for example, heating with a heat pump during the day using cheaper photovoltaic electricity from the roof or that the significantly warmer outside air during the day makes the air heat pump correspondingly more efficient.
For all types of radiators with conventional combustion heating systems (oil, gas, pellets), a night setback is almost always worthwhile, especially if the building is poorly insulated.