The Russian propaganda machine is (just like the American right wing and the American left wing ones) quite potent (I'd argue that the European propaganda machines are weaker, partially simply because most Europeans have far more and easier access to outside sources. I can easily double check what my national TV is telling me on CNN, or BBC, or Bejing Today if I feel so inclined, or Fox News).
If you're a young Russian, you get classes in school to learn how to verify (fake) news stories. Check what different trusted government sources are saying. Check with trusted newspapers that aren't government-owned, like Kommersant (which is....Technically not government-owned. And is allowed to be the "liberal" newspaper in Russia. Which means it makes some minor oppositional sounds on occasion...like, "this special military operation was necessary, but regrettable, such a shame we're being forced into it" instead of "this special military operation is patriotic and we should all be in favor!").
Then you go on VKontakte, where plenty of celebrities and "innocent", "normal" people influencers are using the same talking points - some the official literal words (from which you get those funny composite videos of 100 people repeating the same stuff verbatim, much like local news in the USA). Others, who are "individual" and "open" and "different", use different words and give a slightly different look, but of course the base message remains the same - the people don't agree with the SMO are painted as the absolute lunatic fringe. What they differ on and cause a bunch of noise about to keep critics and opposition occupied is side-stories like "this clearly shows we need more/less money spent on our security", "we should have kept our market closed so we'd be much better off, see how much those evil American corporations can hurt our normal everyday people because we've allowed them in and push away Russian companies", "Western aggression is much worse than we ever expected, see how they instrumentalize economics to try and hurt the Motherland",...). Next you go watch TV, and the official channels, of course, all parrot the official points. So you go watch some commercial TV, where professors and specialists come and explain why and how this is Western imperialism and Russian defense - or is it Russian intervention on behalf of the poor Russian-speaking Ukrainians being killed for almost a decade now? It's all geopolitics, Russia was getting too strong, the West is scared and used this humanitarian action to try and bring us back down.
Wherever you turn, you see the official version. If you don't buy into that and go looking for counter-voices, you'll find them....but they're still actually government-controlled or influenced, and they'll "disagree" on specific aspects while ignoring the baseline.
I read a story about a Russian refugee in the Netherlands. She complained that her parents had been completely indoctrinated in the Soviet era and still couldn't properly think for themselves, and how her children are now being subjected to the same approach and she can see it take hold of her daughter. The daughter was asked to find info on some war-related story, and it took her 8 pages to find real info; everything before was skewed or faked in one way or another.
Having to go to page 8 of search results to find some foreign weird page proclaiming"we're telling the truth and all the rest is lying!", that's....well, conspiracy theorist levels of "searching" for the "right" answer. Young Russians will feel they've done their duty and tried to find the truth after two or three attempts, and they'll still believe the Russian story - even if they're vehemently anti-Putin and pro-democratic!