I have a traditional framed e-bike, motor in the crank, rear derailleur, removerable battery. Overall weight looks similar though. iirc without battery ours comes in at 18-20kg.
I've not yet used it with Model 3, but based upon experiences with a Passat Estate, we got the tow hitch and a 2 bike rear rack.
I've twice tried to put it in the rear of the Passat, albeit without removing the front wheel (didn't have the brake caliper 'wedges') and I can say that unlike a normal weight bike, an e-bike of the weight we are talking about here, even without battery, is a bit of a handful to have to stretch and support whilst manoeuvring into the rear. The other issue was that once in, finding a position that did not risk putting undue pressure on some of the moving or more fragile parts (mostly the derailleur so hopefully less of an issue for the S3), and preventing the bike from moving when travelling was also a time consuming task, although with practice would get easier I am sure.
On the few other occasions we transported the bike, a dead lift onto the roof bar, but equally not recommended, especially if just the one person. I'm looking forward to getting use of the bike with the rear carrier this year. I need to bleed the brakes first though.