I strongly disagree with your analysis. If you are a Russian man who is being conscripted to be sent to fight in an offensive war against a peaceful neighbouring country (Ukraine), which you don't agree with, then you are in a very vulnerable position where you are at high risk of being persecuted. If you refuse to submit to conscription and go on the run you will be arrested, beaten up and imprisoned. If you go along with it, but try to creatively find ways to avoid going to the battlefield (conscientious objector etc) you are also likely to get arrested, beaten up and imprisoned. If you try to desert then you will be arrested, beaten up and imprisoned (or shot if it happens on the battlefield). If you refuse to follow orders to torture, rape, kill Ukrainian civilians/PoWs then you will be arrested, beaten up and imprisoned/shot. If you surrender to Ukrainian forces then when the Russians get you back you will be arrested, beaten up and imprisoned. Russian prisons are also extremely brutal places where draft dodgers/deserters/dishonoured soldiers get regular beatings from prisoners/guards.
Therefore, Russian men who are avoiding being drafted to fight in an offensive war against a foreign country are indeed fleeing 'war, violence, conflict or persecution', they are hardly voluntary emigrants like the economic migrants coming here from India, Jamaica etc.
I think that Russian men in that situation should receive political asylum. But, obviously, they have to be checked out carefully so we don't end up bringing in more of Putin's spies and saboteurs.