I have no truth in my hands about this problem but in my experience, as already said, depends from many thing. As like you I have my Magic Keyboard (with touch ID) working and my Logitech ten - years old (minimun) mouse having problems. Before changing the display's HDMI cable with the actual, the actual Magic Keyboard was connecting and disconnecting every 2-3 seconds.
But this was not happening with the previous Magic Keyboard (grey model) without the touch ID. Today I got a new mouse (can't remeber the brand) wich is surely a BT 5.0 mouse. Absolutely unusable! So? It's a nightmare.
I'm hoping a minor release of Big Sur is going to patch the problem because I dont' want to upgrade anymore to further OSes although is not a good practice to keep the first release of an OS that came with the machine you own (in this case, Big Sur with M1 machines). IMHO.