The sounds and instrument indications will vary with engine and aircraft type.
A Spey at ground level will get everyone’s attention, similarly with an A330 at takeoff.
Alternatively a small corporate engine or regional jet, especially with mixed compressor systems may only be a slight ‘bump’ noise.
Most of the problems with simulation are that everyone has their own view of fidelity, yet few question the training point in having the failure option.
It is most unlikely that a crew will be able to identify the cause of a bang, or any other loud noise in isolation. Engine pop surges are often over before supporting instrument evidence can be seen. Longer duration ‘locked in’ stalls normally provide adequate supportive indications, possibly with some vibration.
Thus the point of a drill is to know what the combined symptoms are, how to confirm the event, and to have knowledge or guidance of what action to take.
Many modern engines self-recover from stalls/surges, and can be used without further fault. However, without knowing the cause of the event or if any damage has resulted there will always be a judgment of risk in continuing.