“The battle sealed the fate of the Confederacy”
That’s unlikely. Lee would invade the North again, and the Union had yet to find a general (Grant) who could win consistently. Most people would say the Confederacy’s fate was sealed July 4, 1863, when federal troops carried the day at Gettysburg and Vicksburg.
I would say the fate of the Confederacy was sealed with the death of Stonewall Jackson after the battle of Chancellorsville. The Army of Nothern VIrginia, and thus the South, never recovered from that tragic loss.
But Antietam gave Lincoln the victory he needed to issue his Emancipation Proclamation. By injecting an end to slavery into the Union war effort it ended forever the possibility of European intervention on the side of the confederacy. Without that intervention the confederacy was doomed.
And that fate was sealed by repeating the same mistake that the Britsh had at the Battle of Bunker Hill during the Revolutionary War: you don’t attack someone who has a commanding higher geographic position. Pickett’s charge on July 4, 1863 resulted in essentially wiping out a huge fraction of the Confederate Army, and the British suffered 1,000 casualties (that’s a lot by the standards of war in 1775!) trying to take Breed’s Hill near Boston. You’d think General Lee would have read up on the bloody assault on Breed’s Hill and didn’t repeat that mistake a second time.