I get the feeling the 4 million grain Revolving Peasant Gun with the velocity of 1% the speed of light will have the desired effect on any target.

This is simply true, you do lose potential energy transfer if the bullet exits, that's how it can exit, that's just not usually the point of a bullet, and generally speaking making exit wounds is considered a positive.

Now if you want to design a bullet that explodes inside a wound causing mass trauma and an incredibly difficult surgery to repair it is a problem, but surely no one would ever deliberately design a weapon to do that! /S

Fun Fact: the .50 cal MGs the Soviets supplied to the Vietnamese during the American invasion usually had enough penetrative power to go through the M113 APC's aluminum hull...

Once. And then it would bounce around inside.

Somewhat pedantical quibble, really just because I find it interesting: It's not exactly limited by barrel length. We can make faster burning, higher powered propellants, which you can get the full energy out of with a shorter barrel. The reason we don't is because that means you have a higher pressure inside the chamber and, even if your gun doesn't explode, you face more erosion from use. Your metallurgy ends up being the limiting factor, as it's all about how strong you can make your chamber. I just think it's cool because guns are a great example of how inter-related technologies are and how everything depends on everything else. Take a design for a machinegun back to the Napoleonic era and it will be worthless because without smokeless powder it will jam and clog after a couple rounds. Take back a formula for smokeless powder and it will be worthless because you don't know how to make brass cartridges. Try to make brass cartridges and you'll find you lack the precision tooling, and so on.

No, but if it travels fast enough it would disintegrate and you could argue the resulting plasma blast would be what actually damages the target.

Relevant XKCD (in video form).

Any matter going through you with that much mass is going to cause damage no matter how fast it goes. Billions of particles called neutrinos are moving through you right now as you read this but they are around 100,000,000,000,000x less massive than a hydrogen atom

Only in anime.

Define damage. Can it pass through the middle of organs? Sure, if it hits just right. But that's not so much a question of speed.

You'd need a pin needle shape to have a chance of piercing an organ without causing lasting damage, but it will probably break on impact

Not really applicable but think there could be a small chance it would quantum tunnel through the person but that's such miniscule chance.