Im in Australia and I've just experienced the same issue and as there is hardly anything about swift CVT failures I have registered and posted here.
We bought the car used, 2012 model, 120,000km, drove it for one day less than 50km, then the trans warning light and check engine light came on. When I tried driving in manual mode it was under and over revving (slipping) in 5th and 6th gear. It was fine in auto mode.
I called the dealer who informed me the trans is a 'sealed unit' and not serviceable. So from that I deduce that if the trans warning light comes on you're up for a new gearbox.
I also find it interesting that the guy in NZ who rebuilds CVT's specifies to only use Suzuki green fluid in his rebuilt CVTs and he sells all the different types of fluids. So if I have to buy another car, if it doesnt have green fluid, I'll pass.
OK, today I got the codes read and my fault code is P0841 "Low fluid pressure at Sensor A". I have spoken to the CVT rebuilder in NZ, and they have advised it could be Valve Body / Hydraulic control unit, or just bad and incorrect fluid. Hopefully this has not caused long lasting damage to the drive belt. Today it is driving perfectly. I could not get it to fault at all: https://www.youtube.com/watch?v=5LPtXmY2ZNU&t=267s