But wasn’t the gunfire from the Civil War still coming from a variation of muzzle-loaded muskets?

They were muzzle-loaders, but they were rifled. It makes a huge differance. Smoothbore muskets weren’t accurate at anything but point-blank range and required massed fire to be effective. Civil War era rifles were accurate to a couple hundred yards, and still effective beyond that. The fact they were muzzle-loaded simply slowed their rate of fire.

t seems like it was still rational during the civil war to pursue tactics of advancing on enemy lines in tight formation until you could engage them hand-to-hand.

It was “rational” at the beginning of the war because there wasn’t another school of thought on how to fight. During the war though it became apparent that their previous experiences simply weren’t as effective. As I’d mentioned before they learned and adapted the use of mounted cavalry and artillery to the new warfare, it just wasn’t passed on to the infantry. Some (a lot?) of that has to do with the viewed “expendability” of the infantry.

Melchett: Good man. Now, Field Marshal Haig has formulated a
brilliant new tactical plan to ensure final victory in the
field. [they gather around a model of the battlefield]

Blackadder: Now, would this brilliant plan involve us climbing out of
our trenches and walking slowly towards the enemy sir?

Abraham Lincoln witnessed tests of early forms of a machine gun:

History

It would not be until the mid-19th century that successful machine-gun designs came into existence. The key characteristic of modern machine guns, their relatively high rate of fire and more importantly machine (automatic) loading, came with the Model 1862 Gatling gun, which was adopted by the United States Navy. These weapons were still powered by hand; however, this changed with Hiram Maxim’s idea of harnessing recoil energy to power reloading in his Maxim machine gun. Dr. Gatling also experimented with electric-motor-powered models; this externally powered machine reloading has seen use in modern weapons as well.

It took commanders forever to figure out that the rifle made all of their previous tactics obsolete when it came to infantry.

But wasn’t the gunfire from the Civil War still coming from a variation of muzzle-loaded muskets? It seems like it was still rational during the civil war to pursue tactics of advancing on enemy lines in tight formation until you could engage them hand-to-hand. The tactic was still effective, it’s just that the casualties were higher. It wasn’t until WWI that this tactic became completely useless in making a dent in the enemy’s position.