same boat. i have an air from mid-2013 and my last upgrade was Big Sur. i may have gotten the upgrade by mistake. since it happened, i am no longer getting any

same boat. i have an air from mid-2013 and my last upgrade was Big Sur. i may have gotten the upgrade by mistake. since it happened, i am no longer getting any patches. and Monterey, of course, does not install. the upgrade app still nags me every now and then that i need to upgrade (to what?).but i do have a 2022 M2 on the side, for comparison. as far as i can tell, our problem is not the operating systems. my biggest problem is with our browsers! or rather, our modern resource hog web applications. i only use my personal macbook airs for the web. and i do use safari, chrome, edge, and vivaldi daily. each dedicated to a single purpose. so, on my M2 air, these beasts load most sites i visit fine. my mid-2013 air, sometimes, struggles opening gmail or youtube. i also never open any fancy webgl application on it. oh by the way, edge, whatever you are doing, you are the best when it comes to youtube ;) and that's my only task for you.