Do you not understand the immense amount of energy and resources required to manufacture a single consumable cartridge?
The point is to avoid that entirely and harvest gravity.
Re-wilding teams already climb far and wide, and this would extend their reach without increasing their dependencies.
Ammo is a dependency.
Gravity is not "harvested", it just stores the energy briefly. Someone or something has to lift the weight for every shot, which requires energy.
It's not obvious whether a trebuchet is better than compressed air, like a BB gun.
Do you not understand your argument is exploring a made-up scenario where we're no longer an industrialized civilization where these things are manufactured cheaply by the billions?
And if you INSIST on making everything completely low-tech and renewable, build a potato gun and use high-proof alcohol as fuel. It'll weigh less and last longer than whatever rube-Goldberg trebuchet design you have.