A user-installed battery is a very common cause of poor performance. kernel_task will throttle the Mac's performance due to the non-Apple replacement battery.
Read CPU usage at 90 percent...sometimes for one of many reports on this site.
By replacing it yourself, you will have forfeited the option to have Apple replace your MBA's battery. $129 includes diagnosis, parts, labor, and a warranty. Apple reserves the option to refuse servicing a Mac that was subject to unauthorized modifications, at any price. That fact permanently limits your ability to have Apple diagnose the other, less likely causes. Presumably, you considered the cost savings worthwhile.
... still more incline to think the update has issues, it only takes to read the issues here with computers that are newer than mine, facing the same or other problems.
I've read them. The causes always belong to the same predictable categories. As I wrote I have a variety of Macs including your exact model and ones even older than it, and they're all running perfectly well. Good luck with yours.