Lucky for you I have insomnia
heheh
Yes, there should be some
slight up and down motion because of the oil clearance.
But when people say 'shaft play' they mean excessive shaft play in that the compressor wheel is is getting closer to the point where it will rub or grind in the compressor housing, which is a bad situation.
Turbos that are wearing have shaft play because the bearings and or shaft has/have worn down a bit and so excessive play results.
Here is a picture of the parts all apart. Notice the bearings. These were really OK but you can get the sense of what wears to cause shaft play.
The bearings are all the way at the bottom next to the divider with is a metal sleeve-like thing with the holes in it.