I don’t think it’s actually just in Big Sur. At the bottom of this post describing how to stop them from hiding traffic, they mention someone did a test on Catalina and ran into an issue with the Messages app:

https://tinyapps.org/blog/202010210700_whose_computer_is_it....

Apple deprecated kernel extensions like Little Snitch in Catalina, so if I had to guess it probably applies there as well.

The OP is about Big Sur.