When Stack of Paperwork enters the battlefield, draw a card.
Combat damage uses the stack. (Combat damage assignment can be responded to before damage is dealt. You know, like it used to.)
Normally, each player assigns a creature’s combat damage and it’s immediately dealt. While Stack of Paperwork is on the battlefield, this assignment is put onto the stack as a single game object controlled by no player, and all damage is dealt as assigned as that object resolves.
If a creature leaves the battlefield, combat damage it deals is dealt by that creature as it last existed on the battlefield. Combat damage that would be dealt to it isn’t dealt.
If a creature that would be dealt combat damage stops being a creature, combat damage that would be dealt to it isn’t dealt. If a creature that would deal combat damage stops being a creature, it deals combat damage.
If Stack of Paperwork leaves the battlefield once a combat damage object is on the stack, combat damage still uses the stack for this combat damage step.
No other aspects of the previous combat damage rules are applied while Stack of Paperwork is on the battlefield. Blocking creatures are still ordered and combat damage must be assigned going through that order, requiring lethal damage to be assigned in that order.