Here's the thing:
Polystyrene is different from styrene monomer.
Styrene monomer has all those bad things: carcinogenic etc.
Polystyrene is a long polymer made up of thousands of styrene monomer units chemically bonded together.
The chemical bonds are nearly as strong as the hydrogen-oxygen bonds in a water molecule.
No-one would suggest that imbibing water might cause you to spontaneously catch fire, because hydrogen is flammable.
In the same way, suggesting that large polystyrene polymer molecules have the same carcinogenic properties as styrene monomer is to misunderstand the nature of chemical bonds.
There are bad things about polystyrene, but those are mostly related to environmental damage,rather than health impacts.
People might possibly be confusing gases emitted by polyurethane ( completely different material) as there are no gases that I am aware of emitted by expanded polystyrene.
The 'expanded' bit means bubbles are blown into the material. That requires a blowing agent. Older types used propane as a blowing agent, but modern, food-use applications tend to use water/steam as a blowing agent.
Nothing to worry about.