I think the best answer here is that there is no simple answer. You're right that it could be considered both a civil war within Ukraine and a proxy war between the EU/US and Russia. In a sense, it is both in spirit- the Ukrainian people are torn between Russia and the West, and have escalated to violence in order to settle that dispute. At the same time, the West and Russia are using Ukraine as a proxy for their own conflict- it is merely a pawn in a tug-of-war that's been going on since the end of WW2. But Russia has essentially erased the line between the two by throwing in it's own troops and hardware.
There are multiple ways of looking at it. You could say that Russia is attempting to conquer Ukraine and is recruiting from the Ukrainians in order to do so. Russia would have us believe that it's a purely civil war and they're not involved, just kinda going "we are pretty great, who can blame them?". At this point no-one's fooled anymore except the people that want to be fooled.
So in conclusion I would say it's not as simple as putting it in a single category. It is, I think, both a civil war and a proxy war. But frankly, this could easily evolve into a direct war if Western troops started fighting in Ukraine too. It is definitely something to be worried about, since Russia seems to be on it's way to outright, honest conquest. But they're hampered by the need for the support of the Russian people, who are, I think, less willing to go to war outright than the government.