Using Magic Keyboard + Mouse with 2 MacBook Pros (MacOS Catalina)

I have two MacBook Pros running MacOS Catalina. On my desk, I have an external monitor and a Magic Keyboard & Mouse. I'd like to easily switch the keyboard & mouse between the two laptops when I connect them to the external display. Right now, I have to re-pair the keyboard and mouse everytime I want to switch. Is there a way to automatically have the keyboard/mouse pair to whichever computer is awake and running?