I'm not expert on the average Russian, I've never been there and I've only talked to a few. But from what I've read I have a few broad understandings that seem pretty firm.
1. The USSR never managed to stomp out the Orthodox faith, but they did a pretty good job of tamping it down and controlling it. By the end stage of the Soviet reign, the large majority of Soviets self-identified as athiests. For some reason this was even more true in Russia itself than in the other republics. And the church that did exist appears to have been appropriated by the state - there is strong documentation that the leaders of the Russian Orthodox Church in the late Soviet period were agents of the KGB. Perhaps this was as much a survival tactic as evidence of malfeasance, maybe they were true Church leaders who cut deals with the KGB in order to be able to run a church at all, but it certainly doesn't bode well for their integrity.
2. When the Soviet Union dissolved, a massive pro-Orthodox movement grew in its wake. Today a strong majority of Russians identify as Russian Orthodox, a huge flip from say 1990. However, 70 years of destroying the social norms and practices of church had its effect, so only about 5% of Russians actually attend church, the rest identify as Orthodox in name more than in practice. This appears less true in the other republics - I get the idea that Ukraine, Moldova, Lithuania, etc. are roughly as religious and church-going as Americans are if not moreso, while the Russians are closer to Brits and other non-churchgoing Europeans.
3. Putin is a chameleon who rides the waves. So under the Soviet regime he was a model atheist who happily served the KGB in all its activities and had no problem with the persecution of the church. But in the 1990s he claimed to have a "religious awakening" in his 40s and became a devout Orthodox Christian with a very close relationship to those same church leaders who have been exposed as KGB agents.
4. The function of Orthodox religion in Putin's Russia appears pretty much the same as in Trump's America, only even more cynical. Putin insinuates that Orthodox Christians as the only true Russians, portrays himself as a defender of the faith, and is willing to act in regressive, discriminatory ways against non-Christians and sexual minorities in supposed upholding of those values. But in reality it appears mostly to be a tool to cement his populist appeal and keep power consolidated in his hands. "Defending the Orthodox" doesn't matter enough to Russians for them to actually attend church, so it might as well be a placeholder for their version of White Supremacy - it's just a signal that Putin supports majority rule and Russian pride and considers "true Russians" to be better than their enemies both internal and external.