I’ve used Steico wood fiber exterior insulation for above grade applications. I also know of Gutex who manufactures a similar product and Go Lab, who will begin manufacturing in 2023 (hopefully, the date keeps getting pushed back).
Steico and Gutex are both based in Germany, I believe, so embodied carbon from transportation needs to be taken into account, but if you include stores carbon these products come out way ahead of other exterior products I’ve seen.
I’ve also heard of hempcrete as an exterior insulation, but I can’t speak to the embodied carbon of that material.