After a long search, I was able to find it. If anyone else is wondering, the Flatpak/Steam Deck Lutris config files are located in ~/.var/app/net.lutris.Lutris/config/lutris.
For some reason, Lutris-installed native Linux games also treat ~/.var/app/net.lutris.Lutris/ as their home folder (e.g. Stardew Valley stores its saves in ~/.var/app/net.lutris.Lutris/.config/StardewValley instead of ~/.config/StardewValley).
If anyone can say why this happens, that would be very appreciated!