The Weapon Type Damage Bonus can appear for all Weapon Types.
Assault Rifle, Pistol, Rocket Launcher, Shotgun, SMG, Sniper Rifle
Like most Legendary Artifacts the Heart of the Ancients has one random Variable Ability out of these 4 Categories.
The Heart of the Ancients is not a Standard Legendary Artifact.
It doesn't have a Variable Ability like most Legendary Artifacts.