My 2001 3.0i did not have any up-down steering wheel motion that I remember, but it did have a disturbing amount of clockwise-counterclockwise rotational free play, whether driving or stopped. Turns out that is a not uncommon problem, caused by the double-u-joint in the steering column. Easily fixed, discussed here:
https://www.xoutpost.com/bmw-sav-for...ring-play.html
Some people seem to solve it by replacing the steering column. I did it by carefully re-tightening the locking screws.
I'd take a look at that joint. Helps to have a helper wiggling the steering wheel while you have your hand on the joint to feel for what is moving. Since I fixed mine (mentioned in that thread), my steering wheel is rock solid in all dimensions, now with 199k miles.