The steering switches connect different resistors across a couple wires that are in the big radio connector harness. Working the switches changes the resistance seen by the radio, which the OEM radio interprets. These signals are not on the can bus. The signals are within the OEM radio connector but on different pins. The interface box provided would convert the resistor values to something the aftermarket radio can interpret (if the radio can not interpret directly), and the interface box would plug into the radio.
How to connect the SWC to your radio as its not standardized, there are a dozen ways. The UART label does not make sense for connecting to the Jeep harness, but perhaps connects to the radio. I am going to guess that there is a place to plug this UART cable into the radio. Otherwise are you sure the interface package you got with the radio includes the steering wheel interface? Many kits have a separate and optional SWC box. Such as the SWI models here:
Bottom line, there is no separate in dash connector to the steering wheel switches, its built into the big connector. The only SWC connection you may need to make is from the interface box provided in the kit to a separate connector on your replacement radio and that not standardized.