I have never made, bought or used an inverter because my electricity is reliable.
Inverters are sold to people who go away to camp, hunt or fish. I don't doo dat.
I think no manufacturer makes a poor quality square-wave inverter anymore, today they are modified sine-wave or pure sine-wave.
A pure sine-wave inverter can use a class-D digital amplifier IC driving Mosfets or it can use a microcontroller to make the PWM.
A modified sine-wave is actually a modified square-wave and it has narrow pulses that reach to the peak voltage of a sine-wave and the peaks have their width adjusted for voltage regulation.
The freqiency does not change.
Here is the waveform and schematic of a modified sine-wave inverter without voltage regulation and with voltage regulation: