Updating software in that fashion on Ubuntu is the same as installing:
sudo apt-get update
sudo apt-get install mysql-server
However, often a distribution of Linux (for example, Ubuntu 20.04) only has one "official" version of software included/built for that version of the OS.
So, minor version updates may not be as simple as running sudo apt-get install mysql server.
However, if Forge uses a secondary repository (perhaps a ppa from Launchpad) that regularly builds newer versions of the software (mysql in this case), then running apt-get install mysql-server may work to do the minor upgrade.
To test that out, you can safely run sudo apt-get update && sudo apt-get install mysql-server (without the -y flag!) and it will tell you if it's about to update the software or not.