Hmmm after some experimenting it looks like you cannot have different effect assignments in different style sections.
On Genos, while in the style creator, pressing DIRECT + A (etc) opens the mixer for that section If you change settings for volume, resonance, etc then EXIT and save the style, the settings are updated just for that section. But this does not work for the effect assignment.
Re your side note : this has its roots more than 20 years ago when Yamaha invented a standard called XG. Remember that processing power was much more limited back then. To be XG compliant, a tone generator had to provide an effect block which had two 'modes' - it could be used as either an insert effect on one part, or as a system effect which meant it applied to ALL parts. As a system effect, the amount of 'send' on each part could be set individually. In this way you could for example have a distortion effect applied to two guitar parts. The variation effect was present on older PSR / Tyros as DSP1, on SX/Genos it's shown separately as "variation effect".