I know there are a ton of studies on this for plant-based medicine in relation to SARS and MERS, but I haven't looked much into mushrooms for this. (Even as an amateur mycologist.)
I know folks have been recommending cordyceps for COVID-19, but not because it has antiviral properties. Given that hunting for cordyceps is about the only safe thing to do in NYC right now, maybe this will be the year I actually find it for myself. (Albeit the species that's common in NYC doesn't have any history of being used medicinally afaik.)