Presumably, if a form of carbon in the soil is inert, then it doesn't do much to help agriculture, although it would be sequestering carbon. Organic matter in the soil will be normally be decomposed fairly quickly by soil bacteria and fungi, and these nutrients will be available to plants; dead plant matter then goes back onto the soil.
Edit: the Nature article linked above said "Biochar incorporation can increase crop yield by ameliorating soil physical structure, improving nutrient availability, and enhancing microbial activities"; whether it does this without decomposing, I'm unclear.
I believe there is also a nutrient capture/retention/release benefit from using biochar… it can keep beneficial compounds from washing away too quickly for a plant to make the most of it.
The biochar can be inert, while still providing a benefit.
wild guess here, but it's probably helping with drainage? much like you'd use perlite, moss, coir, etc. improving nutrient availability not by decomposition, but by facilitating movement of the nutrients
Edit: the Nature article linked above said "Biochar incorporation can increase crop yield by ameliorating soil physical structure, improving nutrient availability, and enhancing microbial activities"; whether it does this without decomposing, I'm unclear.