3D Printed Sphere, How to Remove Roughness
While Trish is completely right that the roughness can't be completely eliminated (you can't print a perfect spherical surface with discrete layers), the situation can be improved dramatically. The most telling photo in your question is the one of the removed support structure.
The part of your sphere that's seriously rough is all severe overhang. In this region, the outer wall of layer N+1 barely overlaps the outer wall of layer N, if at all, and without support would be printed mostly or entirely over thin air, failing to attach to anything and sagging/curling down randomly according to tensions in the extruded material, air currents, etc.
Now, with support material that's not entirely the case. Every so often (looks like a 2 mm grid) there are support lines under the overhanging outer wall. These will anchor it every so often and keep it from curling or sagging too much, but they don't actually constrain it to the place the slicer wanted the wall to go, and they don't provide a surface for the extruded material to press against to get the desired (e.g. 0.4 mm wide by 0.1 mm thick) extrusion cross section; instead the cross section will tend to be circular as a result of tensions within the molten material.
In order to get a decent surface over support material, you need what slicers call &quot;Support Interface&quot; or &quot;Support Roof&quot; (these are the names Cura uses; I suspect it's similar in Prusa Slicer). This feature builds a top surface as part of the support material itself for the supported part of the model to rest upon and press against. Of course that can make support harder (potentially a lot harder) to remove, and depends on tuning the Z distance between the model and the support as a tradeoff between quality and difficulty of removal, but it should get you much better results.