The egt also helps diagnose leaks in your “after-cooler” or also know as “charge air cooler”, if you have excessive leaks your temperature will rise, in turn your turbo and exhaust manifold will obviously run hotter and not produce max HP.
All three of those gauges are related to some degree.
Your exhaust temp will also show different temps depending on the probes location, pre turbo temps will absolutely be higher than post temps, on an average the difference would be about 300* hotter pre turbo.
If you install a Pyrometer pre turbo make sure you get all of the drilling’s cleaned out, otherwise it’s headed for the turbine blades on the hot side of the turbo, not good! All of my trucks had the pyro probe after the turbo.