I resolved my problem. Not only had I recently updated to Big Sur, I also had recently began using ExpressVPN. After turning off the VPN, AirDrop became immediately available.

I am having a similar problem, e.g., a short time after updating to Big Sur 11.1, I found I could no longer AirDrop a Photo from my iPhone 8 to my Macbook Air. I select a photo, select the share icon, select the AirDrop icon. But when I select my Macbook (the only device listed), it simply shows that it is "Waiting" and eventually it gives up. I have tried everything mentioned in this thread, to no avail.