Are there types of standard coaxial cable with a propagation velocity of 0.9c? What would be the application?

Air lines still exist, with velocity factor very close to 1.0. These are AFAIK mainly used in old-fashioned VSWR measurements. The advantages are that the dielectric constant of air is fairly stable and well-known, and that you can insert a probe (a tiny antenna) into the middle of the transmission line without damaging the dielectric.

ePTFE (aka "Teflon foam") dielectric typically gives a velocity factor of about 0.85. These cables are, in my experience, used because they maintain low loss to fairly high frequencies and their phase delay is quite stable under variations of temperature and flexure, not specifically because of the high phase velocity. I've used them in test and measurement applications, and I imagine they're also used in things like radar and avionics.

I found a reference saying that "foam polystyrene" dielectric gives a velocity factor of 0.91, but I have no experience with such cables, and I don't know what applications they're favored in. In fact I couldn't (with 2 minutes googling) find any vendor actually selling them.

The high propagation velocity would be a "side effect" of more desirable property - signal loss/dissipation along a cable. Losses are dependent on properties of isolation material. If you already have the best low-loss material, the next thing is to make it porous, so it will mostly contain dry air. The higher propagation velocity is a side effect of this.

Some (older?) coaxes suspend the center conductor with glass beads every so often. Thus most of the dielectric is air. Propagation velocity is almost 1.0 \$c\$.