Do you use it as a laptop, or is it hooked up as a desktop for the most part? If the former, I'd try one of the M series in the same role and see if you notice a difference in ergonomics.
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.