Why don’t they break this sample to pieces to hopefully demonstrate real levitation?
My guess is that they already broke it to pieces and this one levitates slightly. Until they get more samples they will keep this one intact.
They could more or less easily demonstrate levitation even with the current sample, by using four (maybe slightly stronger) magnets. Four magnets are needed so that the sample doesn't float to the side. Typically four magnets are used to demonstrate diamagnetism of e.g. pyrolytic carbon, see the picture in https://en.wikipedia.org/wiki/Diamagnetism
So in summary, they don't show levitation because that's scientifically not needed. It would be much more impressive for the non-scientist however, so I guess eventually they will show this. I assume another reason they didn't do that so far is that they are afraid to lose the tiny sample :-)
Some superconductors will float and stay over just one magnet, but it's a different story: https://en.wikipedia.org/wiki/Flux_pinning - LK-99 is not of this type as far as I know.