Barbarian Rage - While in a rage, Barbarians gain a bonus to strength based weapon damage rolls that increases as they gain levels. This bonus damage is of the same type as the weapon.
College of Swords Bard - Slashing Flourishes add a Bardic Inspiration die of damage of the weapon's type to a weapon attack.
War Domain Cleric - Divine Strike adds 1d8 damage of the weapon's type to your first hit each turn at level 8 and 2d8 at level 14.
Dueling Fighting Style - This fighting style gives a +2 bonus to damage rolls while wielding a melee weapon in one hand and no other weapons. This bonus is of the same type as the weapon.
Battlemaster Maneuvers - Several battlemaster maneuvers, including Sweeping Attack, Trip Attack, and others allow you to add a superiority die as damage of the weapon's type to the damage of a weapon attack.
Rune Knight Fighter - The Giant's Might feature allows a Rune Knight to deal an additional 1d6 damage with weapon attacks and unarmed strikes once per turn. This additional damage is of the same type as the weapon or unarmed strike and increases to 1d8 at level 10 and 1d10 at level 18.
Way of the Kensei Monk - The level 6 Deft Strike ability allows you to spend a ki point to add a roll of your Martial Arts die to the damage of an attack with a kensei weapon. This additional damage is of the same type as the weapon's.
Hunter Conclave Ranger - The Colossus Slayer option for Hunter's Prey at level 3 allows you to add 1d8 damage of the weapon's type to one weapon attack each round that hits a target that is below its hit point maximum.
Gloom Stalker Conclave Ranger - The Dread Ambusher feature allows you to make an additional weapon attack on the first turn of combat when you take the attack action. If this attack hits, it deals an additional 1d8 damage of the weapon's type.
Monster Slayer Conclave Ranger - The Slayer's Prey feature allows you to deal an additional 1d6 damage of the weapon's type once per turn when you hit a designated creature with a weapon attack.
Hunter's Mark - the Ranger spell Hunter's Mark allows you to add 1d6 damage of the weapon's type to any weapon attack that hits the marked target. Other classes can acquire the spell through the Fey Touched feat.
Variant Ranger Feature - The variant level 1 feature, Favored Foe, presented in Tasha's Cauldron of Everything allows a Ranger to deal additional damage of the weapon's type once per turn when the Ranger hits a marked target with a weapon attack. The damage starts at 1d4 and increases at higher levels.
Rogue's Sneak Attack - a Rogue's Sneak Attack adds damage of the same type as the weapon used to deliver the sneak attack.
Dragon Slayers, Giant Slayers, and Corpse Slayers - These magic weapons deal additional damage of their type when hitting Dragons, Giants, and Undead respectively.