As someone who lived in Russia, it’s complicated. Some people swallow the propaganda wholesale, but they are the minority - most are just cynical and are conditioned to see ulterior motives in everyone and everything. So when the TV tells them to distrust someone (the West, Ukraine, opposition politicians) they are generally easily persuaded, but convincing them that the government wants to do something good for them is harder by order of magnitude. Putin is getting pilloried in the social media.
The videos I’m seeing from Russia in the past 24 hours it’s clear no one is buying the government’s assertions that the war is going pretty well and only people with prior military experience will be mobilized - and sure enough, it looks like everyone regardless of experience or family status is getting draft notices, that’s why the Vnukovo airport looked like this yesterday: