>>Did Europeans want the US-NATO to stay?
Good question. Long answer coming up.
Starting after the Berlin wall fell, the US has been drifting away from not just NATO but maintaining the Bretton Woods Accords. If you don't remember, that was when the US proposed to its WWII allies that it use its navy - at its own cost - to guarantee international blue water trade and opened up its consumer market to those allies. The other option was to become an occupying empire, but the US is a naval power. Even if it wanted to do this, it lacked the personnel.
At the time it was also a move to guarantee its own energy supply transport from the Middle East.
The US now has plenty of domestically produced oil for its own consumption. It's become a net exporter in a minor way. Natural gas is a waste product of shale oil production, so no need for a foreign supply of that either.
It's still paying to support those accords, but with less enthusiasm (seems to be what the "America First" movement is all about).
Consider what happens to the rest of the world as the US stops protecting blue water trade for everyone. I suspect members of the EU have and they're doing what they can to keep the US involved.
As far as which side refused to negotiate, it's unclear what happened there. Putin kept asking the US for a guarantee that Ukraine could never join NATO. The US position was that it was entirely up to Ukraine and the other members of NATO and that it didn't have the power to order NATO to admit or not admit. Meanwhile Zelensky kept asking to meet with Putin (seemed clear Zelensky might offer something starting at neutrality - and maybe so far as Finlandization). Putin never took the meeting, kept insisting he wouldn't invade - until he did. Meanwhile, the US kept revealing Putin's preparations / military plans to invade in an effort to get him to not follow through on those plans, Then he invaded - and the US was done talking with him.
Russia was going to collapse on its own - just look at the upside-down demography. It's a nuclear power. If Russia and NATO ever end up in a direct conflict (probably at the Ukraine/Poland border) it will be very one sided. To the point that Russia might use a nuke out of desperation. So anything NATO can do to help Ukraine stop Russia - short of direct conflict - before it gets to that border is going to happen. Weapons systems. Shared satellite and communications intelligence.
