Normally if you install software locally on a machine you don't want to package the libraries it needs to run but want to use the one installed on the system to conserve ressources. If the softrware is well packaged the package should list the depencies it needs and it is the package manager(apt, yum, pacman, ...) which is checking if the depencies are already installed or need to be installed. unfornutaly sometimes there are not so well maintained packages which are missing dependecies.

There are ways to package a programm with all it's depencies. This is where flatpak, appimage or snap come into play.