After getting my 2015 macbook air 11' I am still struggling to find a reason to replace it. Still going strong with no hiccups!
MS Office has already stopped updating, along with some other software (though not much, most still updates without issues). As long as Firefox keeps receiving updates for my system, most things will be fine.
Looks like the only issue with your MacBook Air is there may be some metal issues. https://github.com/dortania/OpenCore-Legacy-Patcher/issues/1...
If those don't look like a problem for you, I'd definitely suggest giving it a try. MacOS 13 should give you at least 3 more years of use out of it.
Going beyond MacOS 13 I don't think is worth it. MacOS 14 is noticeably slower on my 2010 iMac, and there aren't any new features it can take advantage of anyways.