This is an important topic. Some EU countries like Czechia are even blocking visas for Russian citizens now and I think this will be a trend in other EU countries.

AFAIK, since Russia is the aggressor here and is (on paper) a democratic country (but not really), then its citizens are not considered yet victims of the war, and are most likely not falling under the rules of refugee status, unless they can clearly prove that the Russian government is a threat to their life, which would be a bit difficult (like if you're in political opposition to Putin).

I honestly don't envy the Russian people now. They're forced into a conflict they don't want to be in, and are suffering the consequences.