This is a problem with projectors doing HDR because you need to achieve at least 1,000 nits of brightness to get decent HDR. So companies like Sony have created 10,000 Lumen laser projectors that solve some of those problems.

The other problem what is projected can't have the pixels dimmed individually like an OLED screen. It is literally fighting physics at this point. Even if the projector is dimming those pixels the two pixels side by side are going to bleed into each other because it is bouncing off the wall and back into your eyeballs.