Hi, I'm Tiri, one of the game contributors. The reason scars are more common in classic is that the classic game mode lacked the injury system! If your cats are injured and do a good job healing, they can heal without scars
Web version is nearly impossible to update, and thus the inevitable has happened - it's broken. No eta on when it'll be fixed, it's already a miracle it ever worked. But if you're on a computer, download the game and it should work great! If it's not, go to the discord tech support :)