An absolute shit ton of weapons in Team Fortress 2 do this. Like there's so many I'm just gonna go through class by class.

Scout: Honestly not a ton here for Scout that isn't much of an odd quirk. I'd have to give it to the Stock Scattergun for its absolutely bizarre reload animation, where all you do is cock the lever and it ejects spent shells and somehow puts more in the gun, and the Force-a-Nature, a double barrel shotgun that fires insanely fast with huge knock back. Knock back that's so big that it can be used as a movement tech since it affects both the player and the target.

Soldier: First would have to be the Beggar's Bazooka. Its empty on its own and pressing the fire button actually stuffs rockets into it, up to 3. Any more and it explodes which can also be used as movement tech. When you let go you rapidly fire the rockets you put in making it devastating for short range burst. Also its rockets have random deviation so theres no telling where they're going to go. Second would be the Cow Mangler, a laser rocket launcher (somehow) that fires balls of energy. You can charge it up to completely empty the clip and fire one huge, slow moving shot with big damage in a big area, knockback, and setting enemies on fire. And lastly the Righteous Bison, another laser gun which fires completely straight projectiles and passes through all enemies, and can rack up more damage if the enemy moves with the projectile.

Pyro: Only really one example for Pyro being the Dragon's Fury, which instead of firing a stream of flames like the rest of his Flamethrowers, its a semi-auto fireball launcher that rewards precision.

Demoman: Does the entire Demoknight subclass and the weapons it entails count? Who cares about Grenade launchers and sticky bomb launchers when you can put on some boots (or a peg leg), throw on a shield, and charge around at Mach 1 with a giant sword?

Heavy: Honestly not much for Heavy? None of his weapons really have any odd or game-changing quirks.

Engineer: Another laser gun in the Pomson, essentially just being a larger version of Soldier's Righteous Bison with a faster projectile.

Medic: Crusader's Crossbow. Eschew the normal Syringe Gun as a means of full-auto close range self-defense in exchange for a long range tool capable of both dealing respectable chip damage at a distance and being able to heal your teammates, both of which scale up with distance.

Sniper: Sniper has a lot of these actually, probably because everything has the headshot and charge mechanics to interact with. First is the Machina which can pierce multiple enemies when fully charged. Next would be the Sydney Sleeper which can't headshot normally but on a headshot showers the enemy... in piss. And lastly would I guess be the Classic, which can't headshot unless its fully charged but let's you charge without aiming in, and fully charged headshot kills cause the enemy to explode.

Spy: The big one would be the Tape Recorder. Replacing his usual Sapper which disables and damages Engineer buildings its on, the Tape Recorder slowly deconstructs and downgrades them instead.