plasma is hot enough that it would melt the casing of the gun (unless you use iridium for the body) but with hard light all you need is a glass bullet with a lazer projecter in it. however the glass does need to be eched in a specal way so 98 ish precent of the light is trapped in the bullet rapidly heating it, also it looks dazeling. (just a note this would probably not work in real life, but nither would a palsma gun) so yes plasma guns don't get made very often in this FTL universe because it would literly cost a fortune to have one made as almost the entire gun would need to be made of solid iridum, also it would probably be too heavy to lift if that was the case.
A glass bullet that somehow contains light? Can't we forget the bullet entirely, and use a sci-fi laser that'll burn you instantly? Or forget the projector bit, make the casing lead/copper and fill it with powder and use much less energy and make it cheaper?
Science handwaves plasma gun heat issues with "magnetic containment fields" to prevent it from destroying the barrel when fired.
In fact, that's what Star Wars uses for their blaster pistols. It looks like a laser but it's actually a bolt of superheated gas being fired out of the gun and used to scorch targets.
I like to think the pistols/blasters used in FTL are just like that as well (you give them a blaster and prepare for a fight) and that the Burst Lasers are actually shooting high-velocity plasma bolts. Hence why you can see, intercept them and also cause fires. Beams are true lasers as they instantly strike.
Plasma sounds deadly when you give out things like high temperatures but at least it's not "Hard light"
A true late-game weapon would be a railgun. Shoots fast, projectiles travel faster than any bullet, really expensive.