What’s the difference between sport and track mode without MRC?
 

Is there a difference in NPP exhaust sound or shifting in the two modes?

Yes, check out this chart. It's for my 2018, but I'm almost certain it also applies to your 2023 with no changes except for the fact that you also have line lock on your SS, unlike 2016-2018 model year SS Camaros.

NPP valve control tables in the tune are different for sport and track mode, the valves stay open in a wider rpm and throttle range in track mode (although they still do close when cruising on the highway, which is why some resort to the "fuse pull technique" to keep the valves open 100% of the time).

NPP sound is different, In my case I don't have NPP so sound is the same, but in Tour mode the vehicle tries to lower RPM's which makes it quieter, unlike sport or track which holds lower gears longer thus higher RPM more sound

Throttle response and steering stiffness (Steering stiffness can be set manually though on the touch screen vehicle settings if you don't want it automatically changed)

Sport has a higher ratio of pedal to power (less pedal more power)
Track is a 1:1 ratio from what people have said on these forums

I use track mode when I'm playing around or at the strip. Otherwise I'm in touring most of the time.