Several aspects here, essentially a stream-of-consciousness memory dump.
It so happens that if you use a tank of liquid, water with some milk added works rather well. You only need one visible laser with fast beam positioning, gating, and focusing. The fat particles in the milk act as scattering centers.
For use in the atmosphere, I recall when my wife and I were motorcycle touring and we ended up spending a few nights on the North rim of the Grand Canyon. There were no towns anywhere near so the sky was really dark. We joined a night tour that was astronomy related. The instructor/group leader used a five-cell flashlight as a pointer to celestial objects. There was enough moisture in the air that the backscatter was easily visible as a beam of light.
If you have seen searchlights used for advertising, it is the same effect.
What you are proposing requires enough energy to excite atoms or molecules to a higher energy state, which then decay to ground state and emit the excess energy as visible light. This is the way Neon signs and lamps work, and also the lasers you are proposing to use.
If you consider how much power your laser needs to operate, that will give you a vague idea of the power needed to ionize the atmosphere... a rather difficult/expensive task, I'm afraid. You would have to start with a large diameter beam and have it focus at the position you want to illuminate, or use multiple beams that converge at the target region. You have to somehow get X amount of energy to a small volume; with X being the energy needed to excite Nitrogen or Oxygen to a higher energy state. I expect that in the U.S. both the Federal Aviation Administration(FAA) and the Occupational Safety and Health Administration (OSHA,
https://www.osha.gov/dts/osta/otm/otm_iii/otm_iii_6.html) would have something to say.
If I recall correctly, there was a military research project many years ago that built a large chemical laser and mounted it in a large transport airplane. A chemical laser because that was the only way to get high enough power. They were trying to develop it as a weapon. It was functional but the effort was abandoned as impractical, I don't recall the details.
Hope it helps... and Have Fun!
Cheers,
Tom
p.s. Just remembered that there are holographic displays that project images in space. Though they are probably not suitable for your present project because they are back projection systems where the laser shines through a hologram towards the observer. The effect is a 3D image appearing to be in front of the observer, i.e. effectively the retina is the screen.