Not that it is any consolation, but my rig has done that since new. It's not loud or neck breaking, but it is a little annoying there is that much play in the rear diff & trany bran new.
Jack up the rear wheels, then rock the drive line back and forth by hand. You can also do the same with both rear wheels. There is play in all of them.
My "U" joints are solid.
I've heard they were made sloppy on purpose. This was to prevent immediate deceleration and acceleration with slight gas pedal changes.
In theory it helps your mileage, especially with an automatic.
Now if it is real bad, then that is entirely different.