The point of turning the trees into Charcoal is to return all the non-carbon elements to the environment and remove any metabolic activity from releasing that carbon.

The USA currently produces about 70 million tons of paper per year, which is about half carbon by weight. We produce about 2 gigatons of lumber per year, which is again about half carbon, all absorbed from the atmosphere.

Unfortunately, we produce like 40 gigatons of CO2 per year. So we would have to scale lumber work dramatically. It's also not a clean industry itself, reliant on heavy machinery running on gasoline or diesel, and turning that wood into charcoal would require massive refineries.

IMO more effective bets are figuring out how to artificially induce massive blooms of algae and plankton in parts of the ocean to essentially recreate the conditions that lead to the hydrocarbon deposits in the first place. There's some work on this right now, but like any massive engineering and ecological tampering, there will be tradeoffs and downsides. I also don't know how you prevent the dead plant matter from decomposing and releasing the carbon.