If your argument hold, then why NATO provide arms to Ukraine to fight off Russia
NATO IS INVOLVED in this war with Russia anyway you want to put it. The amount of Advance of Weapon NATO send to Ukraine is as good as Ukraine being in NATO themselves, if that did not proof there is a vested interest between Ukraine and NATO, then I don't know what will.
And on the other hand, you already risk MAD if you use nuke whether or not you use it on NATO, because again, if the world is going to just condemn, then why other country have nuke? It's one thing you say you will use it, that's a threat, you will treat it seriously because you don't want the other side to use it. it's another thing to actually use it, because that would become an action. Once you have used it. then what next? There are no next, because you can't go up on the threat level, everything else is below nuke. which mean you have already used that trump card, and you are expected to be served with consequence (all in past tense) which mean if you do that,. there are pretty much NOTHING YOU WILL NOT DO. And in this case, there are more urge to end this before it goes out of hand.
There is a reason why Russia is in the shit since last June and have been saying they will be using nuke but didn't. You expected consequence when you do that particular action, you do that, the entire world turn on you, which mean you have to think if that worth it to use nuke.
Ground War? Yes.
I cannot comment on anything else.