The article claims "[t]his calcium carbonate strengthens the biochar" but this runs counter to my understanding and I'd like to see some numbers, particularly versus alkalized biochar that is never exposed to CO2.

How important is binding in compression (which is what concrete is used for)? Not very.

Carbonate doesn't strengthen, it weakens. And if forming carbonate in biochar strengthens versus standard biochar, I would imagine forming oxide in biochar would strengthen even more.