The problem is, you are getting hung up on semantics. Instead of using a dictionary, it is important to understand how the people of the era used the term.
I am a cancer survivor. To preserve my health and my lifespan, it was necessary to cut my body open and remove a part of it. I am not the same after that, but the big picture is, I will survive. I am better offer because this risk that was posed to my health is gone (I hope!).
To preserve the nation, Union people believed it was necessary to remove the threat, the cancer, of disunion, and to defeat those who perpetrated disunion. That removal involved involved the use of violence, the "cutting open" of the United States if you will, and the country is not the same after that. But the Union survived, and does survive. Many would say that the nation has not only survived, it has thrived.
I understand that you might not like this metaphor of secessionists being a cancer that had to be destroyed, at a cost, to preserve the health and lifespan of the United States. I am just trying to explain how they saw it.
If "preserving" the union is a mathematical term ... by which, at gunpoint, the same number of states that made up the country before the election were present for roll call after the war, the union (in that mathematical sense) was, indeed, preserved. But only in that sense, similar to the way that North Viet Nam "preserved" the union of their once undivided nation. We fought for the south and lost that one, too.
BTW, I am a cancer survivor as well, and I have no problem with your analogy.