It appears that my mid 2013 13" MacBook Air (252 gig SSD) I previously owned was "similar" to your model (according to this):
https://igotoffer.com/apple/macbook-air-6-1/
Given that you have had the battery checked out, unless there is another hardware issue (seems unlikely), then there is something "rogue" going on with software.
So, I'll ask my usual questions:
1. Have you ever done any disk cleanup/maintenance/repairs, from a software perspective? You can actually do quite a lot of disk cleanup on your own, and there are some excellent products available (both free and commercial) that can help you with that.
2. Are you making backups to an external device? That task is so, so
critical. If you are doing that, what software do you use for that task?
3. How much space is on your internal drive?
4. Did you check the site:
https://roaringapps.com/apps
to insure that all your third-party (ie, non-Apple) applications are compatible with the various versions of the Mac OS you have gone through?
Speaking of the previous versions of the Mac OS, what were they? Also, have you always done Mac OS upgrades "in place", ie, basically let the "newer" OS overwrite the old one? If that's the case, it might be wise to 1) check out that roaring apps site, 2) perform extensive dick cleanup/maintenance/repairs, and 3) do a backup. Also, make sure you have the latest, full installation file for Mojave, which is now at V10.14.1 (10.14.2 is in beta testing). Depending on how you have done your backups, the process for doing the clean, fresh, "virgin" installation of Mojave, then "migrating"/copying needed "things" from your backup will either be somewhat "easy", or some what arduous.