If you installed from your package manager, I thought it auto-updated your Firefox. Hopefully a Linux person can chime in on what to do when that doesn't happen automagically.

The Firefox 113.0 was released back on May 9, 2023 so if it was a package build on a unknown Linux distro, this may be due to the Linux distro being a older version that is EOL in package updates support.

Short of updating the Linux distro one can try using the Linux tarbal version from https://www.mozilla.org/firefox/all/desktop-release/

There is no installer or package or such as it is just an archive. You extract it and run the firefox-bin in the firefox folder. There is a Firefox icon you can use for a launcher shortcut in firefox/browser/chrome/icons/default/ folder. Do make sure the firefox folder has read/write permissions for the user so you can get internal Firefox updates from Mozilla. An easy way to do this is to have the firefox folder in /home/ if you are the only user.