In Linux Mint the Update Manager is responsible for all software updates, and applying updates requires root privileges.

“Updates disabled by your organization” might look a bit scary but all it means is that Firefox was told to not worry about updating itself.

The internal Firefox updates are only available with the Linux tarball version from Mozilla as this works same as Firefox updates on macOS and Windows. If you use a package build from your distro then it is updated in the package manager.

The downside of using such package builds is once the version of a Linux distro you have is made EOL in software package updates there will be no more package updates including with Firefox so you can then be stuck with a old Firefox version.

You can download the Linux tarballs at https://www.firefox.com/download/all/ for Release and ESR. Just need to make sure the Firefox folder has read/write permissions for the user as an easy way is to have the Firefox folder in Home.