I'd rephrase it as "Europe has already quietly started a (world) war".

Apparently you would, even though there's absolutely no reason to believe the line of causality ("Europe did X, which started the war") that you're implying.

Starting a war from scratch like this (as Putin did) requires agency, and it's very obvious what the source of agency was in this case.

"Ukraine not annexed by the EU".

That's just hyperbole and nonsense.

It was never being "annexed" by anyone (until Russia started invading in 2014).

In some people's minds Ukraine is not allowed to choose its own alliances.