My advice would be to eschew contact with the floor at all, except maybe with a frame covered in thin cork or felt (or silicone pads, if you want them to stick a bit instead of slide). This bottom part of the frame rests on the floor, and you hang the frame with suitable fasteners to suitable structural members in the ceiling.
Ceilings are much easier to patch than floors.
You want the ceiling fasteners to take most of the weight, and allow for a little movement of the entire frame (though if you do this right, the arc allowed at the bottom end will be minimal). But the point is that this is not a load-bearing surface, other than supporting its own mass. It is purely decorative. If you want a structurally sound "wall" it has to be fully fastened to three sides.
Securely fastened on the wall and ceiling, with sticky silicon non-marring pads on the bottom, should suffice for a decorative room divider. Which is what this is, really.
It needs to be said that making hard-to-patch holes in either the floor or the ceiling is an excellent way to not get your damage deposit back once the lease is over. If you are careful with the wall and ceiling such that regular plaster repairs work (this depends on the ceiling, of course) you should be ok.
Think of this as hanging a really big painting. You shouldn't hang anything else on a painting. But it should hang with sufficient fasteners making holes that can be patched. Sometimes paint is a patch!
Note that we haven't discussed the frame itself. This will have to be sized and constructed to accept the mass of whatever it is holding. So you may have to build a more robust "cantilevered" header than you think. The fact that it is supported at the far corner does help, of course. But you don't want this thing getting hit and twisting off the floor, and then torquing the ceiling joints such that it comes down spectacularly around someone's ears.