Our substrate is comprised of hardwood sawdust/wood chips, mycelium & usually some form of supplementation such as organic wheat bran, soy hulls or coffee grounds etc.
By the time the mushrooms have finished fruiting they have absorbed a lot of the nutrition but what remains has a high carbon content and generally hovers around ph neutral.
It would generally be considered brown matter. We've had folks use it to condition clay and poor soils, as a mulch, brown matter layer in no dig, raised and hugelkultur beds and for compost heaps.
Located only a stones throw from our farm, Angus at Kelvindale Growers Garden has a great tutorial for hot composting featuring some of our spent substrate:
A Hugelkultur style bed at Lambhill Stables featuring a layer of our spent substrate (image 4).