If you are holding a backpack when you open a chest it will open a multi-sectioned version of the chest interface that you can open backpacks from, allowing you transfer items between backpacks and chests. While a backpack is opened it can’t be moved, so there is no chance of accidentally putting a backpack inside itself. When you have a backpack open you can right-click other backpacks to open them. Backpacks can be used from inside other backpacks
