Inverter technology
Have a paragraph about that in my bachelor thesis.
Pretty much the only kind of motor where you can control speed (and thus power) via anything other than frequency and physical construction are what I call "physically commutated motors" or basically just carbon brush motors.
Those are noisy and in many applications not suited - like in hermetically sealed compressors.
So many motors were just single or 3 speed or so - all controlled by different windings.
If you could change the frequency of the supply power, you could change the speed of all other motor types.
That's what an inverter does - it's just basically a variable frequency drive.
It takes the AC from the wall, converts it to DC, smooths that DC, then switches the power through certain types of transistors and related capacitors so that an almost smooth sine wave of desired frequency is created.
Since motors love 3 phase power they often just make 3 phase inverters.
Microwaves use basically the same technology - magnetron physics is a lot more complicated than motor physics though.
The technology is basically the same though.
Main hindrance was the cost of switching components.
You have to switch high amperage at very high speed - that used to be expensive.
The first household inverter motor usage I know of was a Miele washer from the early 2000s before the Navitronic - W487 I think?
That was a TOL Novotronic series 1800rpm model.
Mieles parts list says it uses a "Drehstrommotor" - a 3-phase motor basically.
Since then, any semi conductor technology has become A LOT cheaper and with high production volumes, even the most basic machines now use inverter motors.
The reason why inverters in fridges can save so much power is a nature of any heat pump system.
You want to keep the temperature between hot and cold side as minimal as possible - the lower the temp split, the more efficient the system works.
Most of the time, a fridge needs very minimal cooling power.
But then, it sometimes needs very high cooling power - door was opened, fresh food was added, etc.
With a single speed system, you have to balance that - which means you never really run at the optimal speed, so either you are not cooling as fast as you want OR you are cooling to much.
Cooling to much drops your evaporator temperature lower than needed which - as said - drops efficiency.
So, using a well designed control system, an evaporator sensor and an Inverter compressor, you can always control the temperature split and thus the effective cooling power.