The Union decisively wins First Bull Run in 1861

[The Mikado]

The first major battle of the Civil War at Manassas was a huge Confederate victory, leaving the Union Army running home with their tail between their legs, dashing Union hopes of an early win to the war. Does a Union win that July day at Manassas lead to Rebel morale breaking and an easy Union sacking of Richmond? After all, it was only two months into the war and the Confederacy itself was only a few months old, with a hastily assembled army full of officers who had been US Army officers mere months or even weeks before.

If this DOES break the back of organized Confederate military resistance, does the fact that the war ends swiftly lead to a reunited US with slavery at least temporarily preserved? With the South readmitted with, likely, no time spent as occupied territories and no Emancipation Proclamation, the Southern States could block a 13th Amendment. At most, the leaders of the rebellion (military and political) might be barred from holding office, which might get rid of the worst of the militant slave power ideologues like Davis and Stephens out of the government, but I certainly doubt without the vengeful desire to crush slave power as punishment for the war and treason we'd ever get the 14th and 15th Amendments out of that period even if slavery does eventually die.

[The Mikado]

Given the state of both armies that early in the war, even a decisive Union victory at Bull Run in 1861 would have left McDowell in no condition to pursue as the rebel Army of the Potomac skeddaddled off to Richmond. So in no way does it bring the end of the war in 1861. With so significant a change, it's doubtful Jackson gains his "Stonewall" sobriquet, and if he does, maybe General Bee can explain if he meant it as a compliment or insult.

So any Confederate collapse as a result of Bull Run would be political, not military, in nature. As of Bull Run, Tennessee had seceded but not yet formally joined the Confederacy. So it's possible that Bull Run leads Tennessee to attempt a Kentucky-like neutrality.

My impression that one of Bull Run's biggest impacts was psychological, convincing the South that they actually had a real shot at this. The fledgling CSA losing the first battle of the war might convince the CSA that the secessionist cause was doomed way earlier than that sank in in our timeline.