When I try to have the hearthlings move a already placed item, undeploy an item, or place a new item the hearthlings don’t do it. I tried when they were idle and nothing happened, then I tried pausing and resuming the work, however they do still place items when creating buildings.
This could be caused by different things. They can’t undeploy items if there’s no storage or stockpiles that accept that kind of item. For placing a new item they should be able to reach it. It might appear placeable in your inventory, but it might be stuck who knows where and they can’t reach it (would need a savefile to verify this).
As for not moving items, are you trying to move items inside of buildings? Are those items undeployable (like the banner, for example)?