The file system actually work if you play the downloaded version, otherwise if you are playing on browser it only shows the game client files.I'm not sure how it works actually but It can not acess your data via browser. And thank you for playing!
The web build seems to enumerate the browser cache. Because "Run kitty run" caches some information your game was able to show it. There were also folders from a bunch of other web games I played that stored such data and weren't mine