Does a boiler with a higher nominal power rating consume more electricity?

One of the basic facts about heating is that energy is not consumed by the boiler, but by the object being heated. Therefore, an object of certain characteristics: surface, thermal insulation, spatial orientation, room temperature (maintained by a room thermostat) requires the same amount of heat energy regardless of which energy source it is derived from and what is the power of the boiler.
The next important fact is that energy is mathematically calculated as the product of power and time. In the example of electricity, it is probably simplest to explain why boilers of different nominal powers on the same facility deliver equal amounts of energy.

Example: assume that 96kwh (kilowatt-hours) of energy is required to heat an object.
1. case: Installed boiler of nominal power 12kW. Thanks to a room thermostat that maintains the desired room temperature (turning on and off the boiler if necessary), the boiler will operate effectively for 8 hours a day and deliver 12kW × 8H = 96kwh of energy.
2. case: Installed boiler with a nominal power of 24kW. Thanks to a room thermostat that maintains the desired room temperature (turning on and off the boiler if necessary), the boiler will operate effectively for 4 hours a day and deliver 24kW × 4h = 96kwh of energy.

Of course, you should keep in mind the limitations imposed by the power connection, that is, as a rule, smaller buildings have power connections of less than the maximum allowed power, so it is impossible to connect a boiler with 2 or 3 times the power. In any case, installing a boiler e.g. 30% higher power than calculated does not mean that the electricity bill will be 30% higher, but it means that the boiler will work less time, and the measured electricity on the meter will be practically the same.