So for all those reasons Western nuclear deterrence is irrelevant as far as Ukraine is concerned, and not is an overwhelming conventional deterrence realistic (Europe can't and America won't).
The problem was not that nuclear deterrence did not work, more that Putin believed that Russia threatening to use nuclear weapons and him believing western governments to be weak meant that they (western countries) would not help Ukraine with direct military support, let alone use nuclear weapons. Keep in mind that Russian intelligence agencies almost certainly have details of western nuclear protocols.
Now, with regards to N.A.T.O. (well up to when Trump won the election), that's a different matter as far as Putin was concerned.
The situation has changed now though. Russia is not doing very well in Ukraine, their rate of advance has slowed to a craw. Their economy is not doing as well as they say (21% interest rates and a very high level of inflation). And of course Trump is being a chump.
We just don't know what Trump will do. That and what the current U.S. government has said scares the willies out of the European governments.
With regards to can Europe provide an overwhelming conventional deterrence, I would argue that If the European countries got their act together (including the U.K.) and joined up with Ukraine, the answer would be yes. Although it would be a struggle if a war did start in multiple places.
Russia is only making (very slow) progress in Ukraine because they are throwing men and equipment at the front line. This is unsustainable.
Remember, if there was a conflict between Russia and N.A.T.O. air power would have a more significant role. Even without the U.S. air force, Russia would not want to fight a European N.A.T.O. countries joint air force. And it's not about the number of aircraft, rather the number of trained pilots.
It is however clear for all to see (including Putin) that under Trump, the U.S.A. is unreliable. Hence European, N.A.T.O. and other countries that previously relied on American help and support, will now quickly have to work out what to do. And that almost certainly means increasing or further increasing their own military spending and increasing the size of their army, air force and maybe navy.
Plus carefully considering where to buy new military weapons and equipment.