This is not a transmission problem. It's the traction control, vehicle dynamics/stability control these trucks use.
I own a 2022 Nissan Frontier S-model crew cab 4x4. ANY wheel spin will activate the vehicle stability control on these trucks. When VSC activates it takes throttle away from you. You can sit there with the go pedal mashed to the floor and at best it will creep along, trying not to spin wheels. This happens to mine at the end of my driveway, which is quite steep, when it's snow/ice covered. If I have to stop there. I'm going no where, even in 4x4 unless you disable the VSC.
What you are describing sounds like this. You need to disable the VSC during these conditions. On my 2022, the button is down low on the dash, by where your left knee would rest. Try it.