I don't think it will collapse.
Rather, I think it will go through an extremely difficult period, at the very least a recession of the magnitude of the Great Depression of 1929-33.
There is a chance of World War III arising out of the Ukrainian situation. If Putin uses a nuclear bomb, I am certain that NATO would retaliate in kind: mutually assured destruction, which would likely mean a nuclear winter of at least two years. Europe and the USA are trying to use every means they can to prevent that possibility. But Putin is serious and pathological enough to not care about the obliteration caused by a nuclear strike.
However, whoever survives would eventually and with great struggle and suffering, rebuild. I'm feel sure that the European countries would want to remain as a union, and would embrace union with any neighbours who wanted to join them.
Given the population and power of countries the size of China, India and the USA, forming a union of states is the only way for Europe to survive.
I imagine one day the ASIAN countries will form a similar block, and so will Africa and South America.
That's if any of us survive global warming.