Upgrading a 2011 macBook Pro 13" w/ macOS HighSierra version 10.13.6

I attempted to update my 2011 macBook Pro "13(w/ macOS HighSierra v: 10.13.6), but apparently my browser is out of date?!? I desperately need to upgrade to a 'supported browser' for work projects...but when I try to do so, there's no update available because it's 'not compatible'.

Is there any other way to upgrade my macOS/browser besides this process or is this ol' warrior just past his prime?!? Any advice would be much appreciated!