I can setup a supply line to share crafting material between settlements. But does this also share any buildings/crafted entities I stored in the settlement?
If not, is there some other way to move them between settlements?
No, they do not. This is easily tested.
I stored a turret at the Red Racer garage, and couldn't place it in Sanctuary, even after setting up a supply line.
I haven't found any other way to move them.