If you want to use the in factory in dash display, you first need to confirm you have the video inputs (above your 7 pin trailer connector, option code ZM1). If not, I haven't heard of anyone retrofitting the video inputs and you will not be able to use the factory in-dash display.
The factory supported system is digital video and power over coaxial cable, using Fakra connectors (related to SMB connectors), the same as the other cameras in your truck. Your trailer is likely pre-wired for an older and more universal analog camera with video on coax with RCA connectors and a separate power feed. These will not work with the factory display. I would assume only the GM accessory trailer camera will work with the factory display. You MAY be able to change the connectors on the trailer's wiring to support the GM camera, depending on the size / type of cable.
I have a
tread on adapting the digital rear view mirror to a trailer rear view camera. Overall I'm quite happy with the result but an adding an aftermarket system will be cheaper and easier.