United Kingdom

Your also assuming Putin would use nukes in these scenarios. Both are assumptions. It's inappropriate to plan for one assumption, especially when the consequences are that significant and the insight is low.

If Putin thinks he can beat NATO or get some benefit from fighting NATO he will. Even if this is just negotiation to strengthen his position in Russia. For example a fight with NATO would allow Putin to negotiate an end to war with Ukraine without losing face for the Russian armies poor performance in Ukraine. He tells has the narrative a NATO stalemate caused the peace negotiations that had Russia leave Ukraine.

This type of conflict is more likely if Trump wins. He's anti NATO, a conflict would test the commitment of the US to NATO. It is possible the US doesn't commit to defending European NATO members. Putin would hope that NATO unravels. The unravelling of NATO would be his legacy (in his mind).

NATO is too dependent on the US. So strengthening Europe would be increased commitments from European countries. This makes NATO unravelling less likely as it won't be dependent on the US.

If Putin operates on these assumptions. Then he can start a ground war with NATO without nuclear weapons. The other nuclear states in NATO either store American weapons or have spite retaliation weapons. Nuclear weapons are lose lose, so Putin is unlikely to use them unless his loss is guaranteed.

If we assume it will all end in complete nuclear exchange, anyone operating on another assumption will have the upper hand. Europe needs to keep the US engaged with NATO and simultaneously reduce their dependence on them.

The USA global dominance is under threat. As a consequence the liberal order of the world is under threat. For all their ills America is better than most when it comes to world powers. Russia was cruel to those under its control, Colonial Europe deadly exploitative, the Mongol horde terrifying etc. If you care about liberal democracy, individual liberty and rule of law then Europe needs to defend these values. The assumption that the world is heading towards democracy and freedom is over, it know looks like a post war daydream. China, Russia, India and other emerging powers are increasingly authoritarian and populist. The west is seeing similar motion in their local politics but we are still liberal and need to defend these values or they'll expire. Afghanistan and Iran has caused the west to lose confidence in spreading liberal democracy, but we should not stop defending it. Nuclear weapons aren't necessary to defend it, they also aren't necessary to attack it. Both Russia and Israel have nuclear weapons and involved in conflicts that would be expedited with their use. Neither has used them or looks to use them. Because the outcome is lose lose.

Putin might be very powerful in Russia. But if he tries to launch Nukes his bodyguards and people in the chain of command will recognise such a command would cause them and all their family and loved ones to die. Refusing the order becomes easy when the alternative is certain death of yourself and family.