This is not that complicated... below are the facts as we know them currently -
#1 all SC models are pre-wired for a trailer harness. The pig tail pictured above allows for adding such a harness, its totally plug-n-play, anyone who can use zip ties can do this job.
#2 the currently available 4 pin harness just runs the trailer's lights. If your trailer's weight is under the limit, OR your state doesn't require trailer brakes, OR if your trailer has no brakes (like mine) your good to go at this point.
#3 if for any reason #2 doesn't apply to you then you need a 7 pin connector plus a brake controller. This gives you the extra wires needed to control the trailer brakes plus power the trailer lights.
#4 the 7 pin harness is not available yet from Hyundai, but the part is coming (part# K5F61AU400) welcome to owning a brand new vehicle with limited support and parts during its launch. However a Kia part (#S9F67-AC500) is available that appears to fit. This should be plug-n-play.
#5 you can convert a 4 pin to 7 pin via an aftermarket plug-n-play harness. Head off to Amazon and you'll find plenty, just make sure its not just an adapter but actually has the wires required to install #6. For example this one:
Amazon.com: CURT 57672 Dual-Output 4-Way Flat Vehicle-Side to 7-Way RV Blade Trailer Wiring Adapter , Black: Automotive
#6 to actually control the trailer brakes with the 7 pin you need a separate brake controller. This is a little black box that does the magic. Hyundai not does make any such part so it will have to come from the aftermarket.
#7 normally the brake controller is wired under the dash with a knob of some kind to adjust the sensitivity and power of the brakes. We don't know if these wires are available under the dash on the SC yet.
#8 to eliminate the problem of #7 you can get a wireless controller.
#9 no reason to reinvent the wheel as Hyundai Palisade owners went thru this 7 pin brake controller pain already, they've done all the homework for us, follow their advice:
2021 7-pin harness
If I'm wrong (happens all the time, just ask my wife) then please correct me and I'll edit this post.