> It's just not clear to me what a losing Russia looks like.

Russia entirely out of Ukraine including Crimea, at least.

> Or what Russia, Ukraine, and Europe look like after the smoke clears.

Hard to predict the future. Ideally, Europe with a more sober energy policy, but otherwise its trend of peace and prosperity continuing upwards.

Ukraine getting a handle on its corruption in order to enter the European Union. In an ideal world, Russia would pay for reconstruction in exchange for normalization.

Russia either remaining a pariah, or wanting normalization, willing to do the social introspection and transformation necessary to become a member-in-good-standing of the global community. Like Germany and Japan did. Speculation is that Putin would not be able to withstand a loss to Ukraine, but that Navalny is not better. Further speculation is that such social transformation is literally not possible in Russian society given that it has been run by all-powerful Tsars for centuries. I remain hopeful that this just anti-Russian animus given the war, and not actually true.

> it seems to me that our government has an interest in extending the conflict. We're providing just enough weapons and support to help Ukraine not lose, but not enough support to end this already.

Personally I don't think this is an intentional choice, so much as concerns with political fallout. Midterm elections are soon. Biden's opposition already get a lot of traction criticizing the aid so far. Hopefully for global peace, the incoming faction will also understand the need for supporting Ukraine.

Russia is on the back foot, though.

> I can't help but to worry that we're ultimately making the end state worse for Ukraine and possibly Europe if nukes come into play.

Europe and Ukraine have agency, here. It's not entirely up to the United States, and not the United States' responsibility for the outcome. The mood of the people where I sit, about 100km from the Russian border, which includes Ukrainian refugees, is immense gratitude and thankfulness to the US for helping Ukraine. As an American, I feel pretty proud of my homeland! I cannot imagine any scenario where serious people would blame the US for Russia's using nuclear weapons.

As for what that would look like. Well, from my understanding, nuclear weapon use in two forms, strategic and tactical. Strategic nukes are the classic city-leveling bombs everyone thinks about. There is no advantage for Russia using these bombs at all, so their deployment would be purely for terrorism. I strongly suspect without any evidence that NATO knows where every single one of them is and is well prepared for a conventional pre-emptive strike.

The more realistic concern is tactical nukes, smaller bombs and missiles. But again, from my understanding, they do not hold advantages over conventional weapons, and their use would be a shit-storm for Russia.

So, the outcome for Europe depends on the scale, but their use is unlikely. Assuming something reasonably likely, I think it would be nuclear use limited to small yield, by Russia, on Ukrainian territory; leading immediately to humiliating defeat of Russia by NATO and generations of hatred of Russians that will make the distrust of Germans after WW2 look positively like love. But, hard to predict.