I believe I stumbled on the solution. I had the same issue with my 2020 Sierra. I could hook my trailer to other vehicles and the lights worked. Hook it to my Sierra, and nothing. A seven pin tester indicated no power to the receptacle (although I could see very very faint flashing of some lights on the tester). I checked every fuse and all were good. Stumped, I looked at forums for ideas... nothing worked. Then my 5 year old daughter was "helping me" and inquired about the trailer hitch icon when I placed the truck in reverse - trying to be patient, I showed her how it magnified the hitch (I don't usually use this feature). When I put the truck in park, the park brake engaged and I suddenly had all my trailering lights. The display also inquired about which trailer was connected.
I'm thinking it is some sort of technical setting. Back to your trailer normally and before hooking the trailer and lights use the hitch magnification feature. Hook everything up, you should now have power to the trailering plug. Ever since I started using the magnification feature, I have power to the receptacle. If I forget to use the magnification feature the lights don't work on some of my trailers, but do on others??? Simply use the magnification feature and the lights work on every trailer... go figure???!!!