As far as I can understand from reporting, Putin was under no presure to start this war, he was the initiator and driving force. He has near total power in Russia and is surrounded by old KGB cronies and sycophants and has been remote and not a hands-on leader and problem solver. Yes, there are hawks in Russia and imperialism is embedded in the culture, but it is obvious that vast portions of Russian society don't agree with it enough to want to fight for it. This is particularly true of those under 40 who have access to more outside information and news via the internet, most of those Vlad wants to draft and they are voting with their feet in massive numbers.
Russian society still carries the scars of Stalin and Soviet totalitarianism, the ethos of liberal democracy never took hold there among the majority of the population. The mass exodus we see is a result of them losing their vote and power, most of the male population is in a panic. Why should Vlad care what they think, they have no power, he has it through a rigged election and Duma. The Soviet regime and system collapsed, but the sword and shield of the party, the KGB or its remnants were still around, and Vlad was among them.