“battles might be classified as “major” is irrelevant”
It’s not irrelevant that some battles are major and some are not. All battles with more casulties than First Manassas is an objective standard.
That is irrelevant to the simple fact that Confederate forces invaded Union states and territories when-ever, where-ever and in what-ever strengths they could muster.
Certainly, most of the war was fought on Confederate territory but not because Confederates wanted it that way!
Instead, whenever possible Confederates sent forces into Union areas -- in order to gather up supplies and recruits, destroy Union "infrastructure" (as we call it today), and perhaps most importantly, draw Union forces away from Confederate states.
And why-ever would you try to deny all that?
It's simply good military "strategery", practiced by any thoughtful commander.
It proves that the Confederate government (read: Davis) did have some military smarts, and understood what would be necessary for victory.
Of course, in the end it didn't work, but that was primarily because for every one Confederate soldier operating in Union states & territories, there were at least ten Union soldiers in Confederate states.