Same problem. Apple Mac Mini computer with the new Apple Silicon M1 processor and Big Sur 11.0.1, I try to connect it by Airplay to duplicate the screen, the computer detects the TV but the Sony television turns black screen and nothing is seen, nor duplicates anything. With the same television, a week ago, I was using a Mac Mini from the end of 2012 and it worked perfectly. And today with another Macbook Air computer from 2014 and an iPhone from 2018 it works perfectly.

I also had that problem, Mac Mini crashes and goes back to a log in menu. It was because I had two monitors connected, one for USB-C and the other for HDMI. If I unplug the HDMI cable, Mac won't crashes. It must be because the Mac Mini M1 only supports two monitors. I am in contact with Apple technical support, they are trying to solve the problem, they are escalating the problem to higher technicians. They have checked the configuration of the Mac and the router but they say that everything is fine, next Sunday they will call me again, they continue investigating what the problem is.