does the 2015 s3 come with limited slip differential?

I don't think it does hence the development of upgrades such as this:

 
Think a lot of modern cars has a pseudo LSD by using ABS/traction control/esp by braking the slipping wheel(normally inside wheel) therefore sending power to the other wheel. On an open differential the power goes to the easiest wheel to spin and by using the brakes it can send power to the opposite wheel. It’s more a reactive rather than a pro active approach but similar execution. Mechanical LSD obviously works better.
some newer electronic type lsd is more like the haldex coupling but instead of splitting power between front and back it splits it left and right and meant to be very effective.