How can I update my iMac macOS High Sierra 10.13.6?

The current version of Chrome will still work with macOS 10.13.6. See: https://support.google.com/chrome/a/answer/7100626?hl=en

and

https://www.google.com/chrome/dr/download/

Is your iMac a 2012 or later model? If so, it can be upgraded beyond 10.13.6. The model year of an iMac is available at Apple menu > About This Mac.

Lynn Hyndman wrote:

My mac desktop is about ten years old and macOS Monterey does not appear compatible.

If Monterey isn't compatible, Catalina or Big Sur may be. You need to check your model year and compare to the following.

The model year of an iMac is available at Apple menu > About This Mac.

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

Short of buying another computer, Firefox (and other alternate Web browsers) are the alternative.

Are you running a version of Firefox from the Extended Service Release channel? Mozilla indicates that they won't be supporting any version of Firefox higher than 115 on High Sierra – but that they intend to offer security updates for the ESR version until September 2024.

Mozilla – Firefox users on macOS 10.12, 10.13 and 10.14 moving to Extended Support Release