My understanding is that, in the US at least, almost 100% of our paper supply is sustainable forestation, meaning that more trees are replanted on the same managed land than are harvested.
There are basically controlled forests that they harvest 2% of the forest each year, and then replant it, such that 50 years from then, the trees will again be harvestable. Obviously, not all. But its the vast majority of it that works this way.
In terms of CO2, paper sequesters it away a bit in solid objects that we don't destroy, similar to furniture. It will decay eventually though. That said, the fast growing and harvested forests for paper specifically used for books (not disposable paper like tp or paper towels or mail) and lumber sequester more CO2 "permanently" (hundreds to thousands of years) than do old growth forests or rainforests, which are largely CO2 neutral due to decay.