The faceting cannot be eliminated in SketchUp. SketchUp cannot draw actual curves, it can only approximate them with short straight line segments. As @DaveR says, you can minimize the visible and tactile nature of the faceting by creating the arcs or other curves with more numerous smaller straight line segments. Depending on the printer and material, this would probably go a very long way to making the curved surfaces be fairly smooth to the eye and touch. The model complexity would grow dramatically but with something that is overall fairly simple such as this, a 10X increase in model complexity shouldn’t cause much of a concern.
You may be able to increase the segment-count of the various arcs that form the outlines of the S-shaped features, without having to start from scratch. Use Push-Pull to push the upper faces of each of the S features back down flush with the flat main surface. This action should leave the 2D outline of each S shape. Then select each arc in an outline, and open the Entities Info window. There will be a Segments text field. Hopefully you can edit that number to increase it. Do that for each of the arcs comprising the outline of an S shape, to give them more segments. Then Push-Pull the S outline up again to create the raised feature.
Do the same for the other S-shape instances, or delete their outlines and array-copy (using Move and Option/Alt) the initial S feature to duplicate it as desired.