Safari 13.1.2 is the latest possible version possible with High Sierra 10.13.6. To update Safari you will need to upgrade macOS on your iMac.
The model year of an iMac is available at Apple menu > About This Mac.
An early 2009 iMac can be upgraded to El Capitan 10.11.6 but no later version. See: How to download and install macOS - Apple Support
A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version. See: How to download and install macOS - Apple Support
A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to download and install macOS - Apple Support
A mid 2014 and late 2014 iMac can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to download and install macOS - Apple Support
A late 2015 iMac can be upgraded to the latest version of Monterey macOS 12. See:How to download and install macOS - Apple Support
A 2017 or later iMac can be upgraded to the current version of Ventura macOS 13. See: How to upgrade to macOS Ventura - Apple Support
Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html
If you can't or don't want to upgrade your macOS, for security reasons you should consider using a 3rd party internet browser that supports their current version with your older macOS. Two examples are Chrome https://www.google.com/chrome/ or Firefox.