The APS (Avtomat Podvodnyj Spetsialnyj) was developed in the early 1970s as a way to provide greater firepower to Russian frogmen (who had been previously armed with knives and the SPP-1M underwater pistol). It was initially used by Russian armed forces, but has also been sold on the international market since the fall of the Soviet Union.
https://www.forgottenweapons.com/rifles/aps-underwater-rifle/
So is the idea that it shoots mini harpoons? Are they able to hold up to the water resistance better than a standard bullet (which just shatters and loses killing power after about a foot)?
Yeah, the idea is more mass more inertia. Water has more resistance than air so having a higher sectional density from long harpoon-like bullets means better performance at further distances underwater. Still not great, but better.