I assume the thing bike shops use to hang bikes by the seat posts are called vices. I think I remember reading that unicycles should not be put in them. If not, why? And also, uh oh, because the bike shop just put mine in one.
I think the ones made for bikes are called workstands. A vice will tend to crush your tubing. A bicycle workstand will be made to hold the bike by the tubing without crushing it.
i’vew only seen the work stands that grib by the seat post. you should be fine. seatposts are fairly sturdy, that’s why they get clamped and not other tubes.