If when a compressor is replaced, the system is always evacuated, then pressure and vacuum tested after closing the system back up, and then, recharged with the correct weight of fridge gas, and the oil weight that was in the original compressor should have been weighed, then the new compressor's oil content corrected to be the same as the old one.
Then the system should be run to check for operation, not just for cooling performance, but also to monitor/check Hi side and Lo side running pressures, cooling fan operation etc.
Edit:- please understand that the fridge circuit is not charged up to a certain pressure, this gas is a relatively low pressure product, so as long as there is any liquid refrigerant in the system, with the engine not running, the system pressure will always be the same but vary with ambient temperature. If the system pressure rises under that set of conditions, some of the gas or saturated refrigerant will turn into liquid again.
System running pressures will vary with thermal load and the weight of refrigerant loaded into the system, too much refrigerant loaded in will end up with running high side pressure to be above spec and the pressure sensor will inhibit the chilling function.