From what I've gathered so far, repairs/building is now done by Space Docks (including ships like the ark, and maybe the starships?) and controllers and is indicated by a blue line.
So I just captured a Mk V Shield Starship, and it begun rebuilding the hull using the ark and the controller. After that was done it moved on to shields, which seemed to be going very slowly, so I decided to scrap some turrets and build a space dock. The space dock was created in it's self-building phase, but as soon as it was created started showing a blue repair line to the shield starship (and may be contributing the the shield regeneration?). I'm not sure if that's intended or not, I would have thought that during the build phase structures wouldn't be useful.