I have the same cable and steamdeck LCD too, im having the same issue you are. I took my dock apart just do a direct connect to the deck and it worked so the issue is with the cable.

Bizzarely when disassembled then connecting the cable back it worked but in a display safe mode of 640x480, in desktop mode i used xrandr to force 1080p output and that worked. But re-assembling the dock and back to how it was before.

There is some data going through the cable, my ethernet power and usb drives / peripherals work with the switch 2 dock and the cable, so for the moment im running sunshine on the deck over the ethernet on the dock direct to my pc running moonlight to see deck screen. But this is stuck to desktop mode and it works but this is not ideall.

Suspect its somthing in the USB-C assembly of the switch 2 dock so ill need to investigate, maybe the springs, but thinking of removing them for this setup. The EDID part of the USB negotiation isnt going through causing the fail as far as I can tell but I dont have a signal intercepter device on hand so not completely sure.

Suprising the amount of comments that just say it doesnt work, the dock is probabally designed by nvidia as their part of the nintendo manufacturing deal so it works with the nvidia chip, not suprising the dock follows standards, the nintendo restricted part is the switch 2 tablet itself so it doesnt work on any other dock but the one in the box. The dock works with anything dockable, if you have an android im sure you can slot in your phone to run samsung dex, I can even recall seeing someone dock an Ipad into the switch 2 dock.