Rules to use decoupling capacitors

What are the generic rules to use the decoupling capacitors in terms of SCA?
Is it mandatory to have them at SHUNTH side (if the SoC vendor requires them)?
The capacitors can protect (by filtering) against high frequency power fluctuations (noise) coming from other parts of the circuit and make measurement results better.
One would think the capacitors can break the real power trace shape by providing required “extra power” to the SoC but in the case if we measure at SHUNTL side (before capacitors) we can catch all current changes reflected in the voltage drop across the shunt resistor.
Are these thoughts true?

Yeah, mostly. I don’t know if I would describe them as mandatory, but they’re very helpful on the high side of the shunt. They also help by reducing the AC component of the voltage on the high side of the shunt resistor, which makes the voltage measured on the low side closer to the drop across the shunt.