It's certainly not just Putin's war ...
Remember these people are being lied to constantly. Many of them believe the lie that their people were suffering in Ukraine, and they just had an operation to help free them - only targeting Ukrainian Nazis, and not harming civilians. But the evil West decided to fight Russia, while Russia just wants peace.
Of course it takes a closed mind and some mental gymnastics to go along with the Russian propaganda, but people are capable of that, rather than accepting the truth that their country is rotten to the core.
That's not to say there aren't plenty of people in Russia who know they're in the wrong, and don't care. But are lot of them believe the lies.