What I understand... Engine revs, truck doesn't move. Need a few more details. I know you lifted up the rear end but not for sure exactly what all you tested there...
Here's a few questions.
1. Check to see if your shifter linkage is working. Place your cell phone camera on record on ground under the linkage as you operate it in truck. The linkage has a big black rubber boot on it... It's on the driver side of the transmission housing just above the service pan, and above the exhaust. Broken shifter linkage will result in no codes, always in park (at least in your case), the dash will show gear change, but it'll remain in park and behave as it's in park.
2. Did it roll when they put on tow truck or did they have to drag it up on flatbed?
3. Did you try to spin wheels in neutral? Or just in gear with rear diff raised? I assume both tires were off the ground when you tried to spin a tire? To fully check the rear end you need both tires off the ground. I think you know this... but wasn't sure by your post.
4. Any engine codes?
5. What kind of rear end does the truck have? G80, limited slip, or open diff? If open diff with both wheels off the ground the wheels should still spin by hand even in gear (with a properly functioning rear end). Take a picture of your options sticker in glove box. It shows what the rear diff is.
6. State of transmission fluid would be very helpful were you able to check the stick for smell / dark fluid?
Trying to help you isolate problem to rear diff or transmission. Won't be brakes if you select a gear and engine still revs freely.