Wife has a 2012 and I also just had the same issue. There should be a notice to download when you go to help and then about. Here is a link if that doesn't work. https://www.firefox.com/en-US/download/all/desktop-esr/osx/en-US/

Here is what I have. see screenshots Going to help and about, the browser checks for update.

Firefox ESR 115 Where can I download this as I cannot use my Mac air 2013 has no browser expired

What macOS version does it have as you listed O S X 10.8.5 in your system details on the right.

For macOS 10.12, 10.13, 10.14 thje latest you can run is Firefox 115 ESR currently at 115.29.0esr and planned for updates till 115.33.0esr next year unless Mozilla extends updates again. https://support.mozilla.org/en-US/kb/firefox-users-macos-1012-1013-1014-moving-to-extended-support

For macOS 10.9, 10.10, 10.11 the latest you can run is Firefox 78.15.0esr https://support.mozilla.org/en-US/kb/firefox-mac-osx-users-esr