There would be no "victor" in such a conflict. The Union would simply disintegrate and you'd have loose coalitions of Independent Republics littering what was the United States.
No, that's not how these things play out. The losing side has committed treason -- as defined by the winning side -- and will be politically swept aside. Neither is this a situation that can be dragged out, as with the (first?) Civil War. Once a majority of the armed forces pick a side, this becomes either emergency police action against insurrectionists (cf. Andrew Jackson's threat about 'seceding Calhoun's head from his body' over the nullification crisis), or emergency police action against a criminal admistration turned tyrannical. The side that is declared illegitimate, by the side that can back that accusation up by force of arms, is the side that loses pretty definitively.
If this comes to shooting and the Republicans back down or are successfully branded traitors, then no Republican will hold serious office in the USA for the next two or three decades. If it comes to such extremes and the Biden administration loses, then the same holds true for Democrats. In either case, the winning side will be -- if not dominated, then at least strongly influenced by it 'extremist' wing. Which will mean that the winning side carries out fairly significant reforms.
A Democrat victory, for instance, would mean that the Second Amendment is (functionally or literally) nixed, the Supreme Court is packed (and/or the sitting conservatives are branded traitors and evicted), abortion is guaranteed on a federal level, MAGA-aligned groups are banned, members of such groups are convicted for domestic terrorism purely on the grounds that they are members... and, of course, the Federal government assumes effective control of everything and the states become mere provinces that have to shut up and obey. Plus, border control becomes functionally meaningless.
A Republican victory, conversely, would mean the opposite. A major return to states' rights (probably via Constitutional amendment), removal of key Democrat functionaries for their attempted "coup", most or all gun laws immediately declared unconstitutional, probably a federal abortion ban, and mass terrorism charges against left-wing groups. Plus, borders become functionally closed, and will be heavily patrolled with soldiers with standing kill orders.