Here is the all-time leaderboard: https://docs.google.com/spreadsheets/d/1ev7koC1JQRy_FCk4VZ7vxDrKzI0VF2Fqsk9g4m8l...
2:38 is currently the best time. I have theorised with the current route the best time probably lies at 2:36 but you'd need the propper screen and muscle memorie for scrolling. The reason for the time also has to do with touch screens. They allow for simultanious button presses. Unless someone finds a new route or a TAS is developped to test all possible routes 2:38 will not fall without hours of dedication to the current route.