It’s hard to say as there aren’t any reliable (and independent) social analysis on the matter. I live in a bubble where everyone is strongly against it but it’s not a representative group.
Going just by my personal experience I don’t think that many actively support the war, most people try to go by as if it wasn’t happening at all — and it’s a viewpoint that is actively encouraged by the actions of the government. But this apathetic majority allows Putin to do what he wants.
As for the support of Putin, it’s more complicated. The most ludicrous yet popular opinion that I’ve heard a lot during the election was “we have a war and only a strong leader like Putin can end it, so we must vote for him”… completely missing the point that it was Putin who started it.