When you format it, you erase all the permissions. All you need to do is give yourself permissions to solve this issue.
sudo chown -R user:user /mnt/media/scott
Replace both users’s with your actual username.
Two things:
- exFat doesn’t actually have those permissions so you weren’t the owner before. It just looked like you were due to the mount options.
- You probably didn’t format it as your user account. Accessing the underlying device to format it would normally require root permissions. If gnome disks didn’t ask for a password to do that, you must have some polkit rules allowing it.
Lastly, for someone like you, who likes to understand things, using gnome disks for these operations is probably a mistake. The nice thing about gnome disks is it “just works”. However, it is abstracting what it is really doing so you don’t get to have an understanding of it. For example, if you had mounted that exfat drive yourself, you would have realized how the permissions were being set.