I’ve been stuck this bad on my ranch. To get out, you have to leave it until it stops raining about 12 hours. At that point, it will be dry enough for the tracks to get some traction but not be frozen in place by too much drying.
About 12-18 hours AFTER the rain stops, you can drive right out.
The trick is getting in the cab as the door will likely be blocked by mud. That’s shovel time.