Would you keep the module when you lose the artifact? I don't know if there would be errors from setting an ability back 1 stage such as self destruct level 2 back to level 1 if it was the last thing upgraded just as an example.
As far as artifacts...
Increase crew experience, increase ship speed, decrease mass, increase planet health( or planet health regen), increase logistics/tactical build speed, increase fleet supply, increase relationships, decrease cooldown (ship abilities), increase extraction (mining), increase explosives damage (mines / missles / planet damage).
Trying not to rip off of race specific bonuses, although essentially all of the artifacts do that.