No option for the Switch version, but I guess this should suffice.
Anyway, it appears that when I close the app and re-open it, most of the system data isn't preserved. I still have run data, and I can resume the run that is in progress. My entire compendium is wiped, I no longer have the second character unlocked, my Mettle is gone, my Prestige is gone, and when I resume my game I get the tutorials thrown at me again as if I'm playing for the first time.
Is it perhaps possible that system data is never saved?
Start the game. Play a while. Exit to the game's main menu so it saves the run data, then close the game from the Switch's main menu. Then open it again.