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Quick Question: Are set bonuses considered enchantments?
For the purpose of the question, no. The effects of a set bonus is a magickal characteristic imbued (and stone carved) to it.
However, although I never saw it, some sets, maybe specifically when weapons, might have its characteristics boosted, like... an Infused Master/Maelstrom weapon, if such thing exists.
I am the very model of a scientist Salarian, I've studied species Turian, Asari, and Batarian.
I'm quite good at genetics (as a subset of biology) because I am an expert (which I know is a tautology).
My xenoscience studies range from urban to agrarian, I am the very model of a Scientist Salarian.
Set bonuses are not enchantments, the amount of bonus you get is based on whatever your lowest quality equipped piece grants. Say you have 4/5 Pieces that are Purple quality giving you 60 regen, but you have the 5th piece green quality giving you 40 regen; the entire set will give you only that 40 regen as its your lowest quality piece. To get the 60 regen you have to have all 5 pieces equipped purple or higher.
Level and quality are afaik the only factor that affect trait bonuses.
Also, it's worth mentioning that set bonuses do scale up quite a bit in battle leveled zones such as all DLC, vet scaled dungeons and cyrodil. So if your crafting/buying gear for PvP for a low level character especially you will notice the bonuses to be greater in cyrodil and other zones where your character is "battle leveled".