When the blue School Backpack is equipped, its inventory is not visible and not accessible from the inventory menu. Loot can still be added to its inventory automatically by the "take" function, but then it cannot be accessed until it is swapped to hands. Items assigned a quickslot can be moved between the hands and the backpack without issue while it is equipped.
Similarly, when the blue School Backpack is in the vicinity and has items inside, the only way to access the items is to take it to hands first.