I thought I was the only one having these issues and thought it was something wrong with the new Macbook Air M1 chip. Within a week of getting this laptop with Big Sur, the trackpad stopped responding to touch, started jumping around sporadically, and clicking on things randomly. It has been a nightmare!
I chatted with Apple Support online, who made me an appointment with a Genius Bar, but the Genius Bar called me shortly after I dropped off my computer for diagnostics and told me there was nothing wrong with it and I should just call Apple Support if it happened again. When I called Apple Support, they said it was clear my computer needed repairs and to tell the Genious Bar I had already called Apple Support and they couldn't do anything over the phone.
So far, no luck and I'm still dealing with an all but useless trackpad...
Hoping for some kind of solution soon!