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

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

In the About dialog, “Updates disabled by your system administrator” has the same meaning.

Mozilla only provides internal Firefox updates to their own builds of Firefox for Windows, macOS, Linux from https://www.mozilla.org/firefox/all/desktop-release/

A lot of package builds do not have this Updates Disabled by System Administrator message and just simply removed the check for updates since you cannot update Firefox that way.