Do guns in Fallout New Vegas use hitscan or fire bullet projectiles?

This depends on the weapon and whether or not you're using VATS.

As you note, plasma and payload weapons are obviously not hitscan.

However, bullet-based and laser weapons are hitscan. From, of all things, TV Tropes :

This is most obvious when, through mods, using a scope on a normally unscoped weapon. The enemy will drop almost a full half-second before the tracer projectile reaches them at long ranges.

In VATS basically everything is hitscan in a manner of speaking: because the hit-or-miss determination is probabilistic, the behavior of the projectile is determined after the hit-or-miss determination which is also how hitscan works. This includes payload and plasma weapons, essentially turning a rocket launcher into a hitscan weapon for that one shot.