Which weapon upgrades affect settlers accuracy?

As discussed on the Steam community forums, NPCs will not use any "active" modification (things you have to turn on) but will benefit from any "passive" modification (mods that are always on - like your statistics on your synth bracers example). The exception being mods like recoil since NPCs don't really experience recoil in the same way that a player would.

It's worth considering that NPCs don't have perk trees so certain weapons are less effective in the hands of NPCs than they would be if you're using them. Through testing I found that simple double barrel shotguns seemed to be a very effective upgrade for NPCs due to their high base damage and cheap upgrades. Combat shotguns were also pretty good.