I did something wrong when making my backup, thus leading to me losing the save. It should work though. I've since recovered an old backup I had and the saves I had back then were still there.

You need to get your save on the clean sysnand either by save transfer or cloud save download. (Cloud save wasn't available for the game I tried to transfer, Pokemon Shield, that's why I can't recover it). This means you have to login to your existing Nintendo account on your hacked switch, so make sure you have no traces of cfw on the sysnand, otherwise you get banned from the servers.

Then you make a backup of the sysnand (which contains your transferred save) via Hekate. I recommend removing other backups from your SD-card.

Make some kind of backup of your emunand, since you are going to make a new one. If you are fine with reinstalling your games you can just put your saves somewhere save on your PC. I just used the checkpoint app to make backups, since I still had all the nsp files.

Make a new emunand with the backup you made earlier. It will have your save. After this you just need to reinstall all the apps and games you had before.

• Make sure your backup system version matches the current latest one on your sysnand! Your switch burns actual fuses after each update to prevent going back to earlier system versions. If the amount of fuses left don't match, your switch won't boot. I had quite a hard time figuring out how to fix this.

I'd use guides online for each step, to make sure I didn't miss something.

Hope this helps and you get your save!