The “real” state government would be one that wasn’t shooting at the rest of the country, at least according to the thinking of the day. After the war, in any event, there wasn’t going to be any going back.
Agree about the not going back. Not sure whether secession (of the state from the US) had common support or not. I assume it did, and I therefore would tend to view the Confederate government of VA as the legitimate one, but I certainly have no problem with WV for seceding at the state level and staying with the Union if a majority there desired to (as evidently they did).