I attempted to measure lag times for an Olympus C2500L. I displayed a digital clock on my computer screen, clicking off seconds. I tried to push the shutter button when the clock moved to a particular time (an even minute, usually). I could not find the lag, as indicated in the images, to be as much as a second.
I tried to get my reaction time out of it by pulsing my finger rhythmically in time with the seconds. I couldn't find a display finer than seconds, and I doubt if a manual operation of this kind would justify trying to measure fractions of seconds.
I have a watch which pretends to display hundredths of seconds, but experiments with that proved that the lag in the watch LCD invalidated any measurements.
If I have time I'll try it with a 2020, and also see what the continuous mode of that camera does.
The Olympus IR remote has about a 3 second lag.