If you have macOS 10.15 as shown in your post, that is also somewhat old. Safari 15.16.1 is the newest version of Safari that will run in macOS 10.15.7. To go to a newer Safari version you would need to upgrade macOS if you can.
The model year of an iMac is available at Apple menu > About This Mac.
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 but no later. See: How to download and install macOS - Apple Support
A 2017 iMac can be upgraded to the latest version of Ventura macOS 13 but no later. See: How to download and install macOS - Apple Support
A 2019 or later iMac can be upgraded to the current version of Sonoma macOS 14. See:How to upgrade to macOS Sonoma - Apple Support
If you can't upgrade beyond Catalina, another option would be to use a 3rd party browser that supports running their current version with Catalina. One example is Chrome: https://www.google.com/chrome/dr/download/