Catalina is still very buggy! Apple messed up big time and even its updates don’t cleanly install. I’m sure that’s your issue here.
Create a bootable external drive with Catalina and update it to the latest. Using it your system should be stable. Then with it as your active boot drive, check that it is not experiencing the same issue. If its good you’ll need to install a fresh copy of the OS. Depending on what you have for apps and data you’ll want to make a backup of your stuff wipe the drive and install from your external drives installer (not the internet installer copy).