For whatever reason it likes to run Proton instead of the Linux native version by default, which is definitely a choice, and based on the fact that that compatdata path includes the Steam AppID it'd load a different folder for the full game when running on Proton. (Demo is 2570560, and full version is 2562130)
Linux native version in and out of Steam and/or the demo should hit the same ~/.local/share/SternlyWordedAdventures folder regardless.