Dwv
There is NO "S" trap. the vent is off the upper level after the trap so it is proper, except for that portion of the shower vent which is horizontal, unless the sink connects to it. There were probably ways to do it more directly without all those fittings, but that is a problem with the installer's experience. For example, the shower could have connected directly to the 3" in the same bay and would not have required the second hole in the joist, and the toilet pipe did not need that "dog leg" in it.