I think this is a Catalina issue as I don't recall noticing it in Mojave.
I just installed the recently released supplemental update for Catalina and have noticed that all the log files in /Library/Logs have been removed after the upgrade. I took a snapshot on a VM and ran the upgrade a few more times just to confirm this is happening - it is.
Before the upgrade I have a folder /Library/Logs/MyComputerName. In this folder is where I put custom logs, including the log file for our update script. That entire folder is gone, and most of the log files under other folders in /Library/Logs are gone as well (though some empty folders still exist).
I read that Catalina has moved system files to a read-only operating system. I'm wondering if that could be part of this problem.
Does anyone know if this is the expected behavior? Is there a better/recommended place to store log files that will survive macOS updates?