Is the utilization of a shipwright aboard a ship at sea considered a free action that can be used once per turn or its own action taking a turn? Alternatively, If I use a crew/ship ability that would grant an extra/same action and have a shipwright aboard, would I be able to use the shipwright for both actions or would I be limited to using it once per turn?
A shipwright doesn’t grant any actions on its own, it just changes where you can give the ship a normal repair action.
Using one isn’t limited to once per turn, so if your ship does gain an extra action (or the same action twice), you could repair twice.