What was your dealer quote on this? In a similar boat to many where I bought a build and stupidly didn't check the options list/car for the hitch.
From what I have heard, retail pricing on the "kit" to add the hitch/electrics is ~$2,000 for those without the NATO plug, and ~$3,000 with the NATO plug.
I haven't confirmed this directly with the parts in my hand, but from what I've been told the "kit" is the hitch itself, the trailer control module (this provides all the light outputs as well as interfaces with the rest of the vehicle to automatically turn off rear parking sensors, modify the ABS and stability programming, etc when a trailer is detected), and the
complete wiring harness to/through the rear bumper. That harness includes the rear parking sensor wires, trailer connection wiring, and, if optioned, the NATO plug wiring from the interior to the exterior.
An enterprising individual could absolutely purchase the cheaper kit and transfer over the NATO plug wiring form their current bumper harness.
This doesn't include labor, if I were to take a complete guess in the dark, I'd assume 3-5 hours for the install as it also involves some control module recoding to tell the rest of the vehicle that there is now a trailer module in place.
All the above information is specific to MY24/24.2 North American vehicles