Confirmed that "All you have to do is disable "Develop tab -> Experimental features -> VP9 decoder", and then restart Safari" fixes the issue. Thanks, @Arun_Kudiyal.

I am having the exact same problem as the OP even with Big Sur 11.0.1 that was just released to developers today. I can copy and paste from my Mac to my iPhone, but not the other way around. Same complaint. I copy and paste with my authenticator app which I can’t do anymore.