Hi Alex!
Within gypsum board, you can reduce the embodied carbon by choosing lightweight gyp (reduced water = reduced energy for drying and associated CO2 emissions). You can learn more about that and other ways to reduce embodied carbon of gyp on the Carbon Smart Materials Palette:
For innovations/alternatives, I can’t think of an example that has the same aesthetic look, but one you could consider is wood fiberboard. There’s also a rice/straw MDF being developed in California by CalPlant. I’m not sure how far out from market they are, though I’m sure more people in this community have info on that: @david @chris1