The warranty is up on my 2016 S Type in Nov-20. I'm trying to get an idea what some of the more common problems would cost if they happen after the warranty expires. Mostly worried about limited slip differential replacement, supercharger issues or anything that might cost over $3K USD.
My car only has 15K miles, but it seems like some of this stuff can show up really early.

 

Differential replacement or supercharger issues CAN happen (among others), but nothing "common." Water pump or Ox sensors might be the most likely, based on forum feedback, but well under your $3k threshold. Personally, I'm a couple of years ahead of you and my non-warranty costs have included fluids and a battery replaced on general principle. YMMV.

Even $3k sounds pretty good compared to the cost of a new car that comes with warranty protection and a certain cost of more like 4x that for a year.