I think your analysis is dead on, but there’s a wrinkle you haven’t touched on.
There’s no reason to think that Putin needs to hold out longer than early 2023.
All he needs to do is hang on til November and let inflation and the nationalist insanity he’s drummed up in America take hold, and like as not Putin will end up with one of the houses of the US Congress, if not both.
That house holds the keys to impeachment, and they’ve already basically said they’d have no compunctions about using the impeachment process to install their own puppet. If they also get the Senate it’s game over. There is also no doubt that wherever possible the GOP will subvert the elections to make sure their candidates win.
Were that to happen, Russia would have effective control over their chief rival, and the only one who could seriously challenge them on their own.
Given China’s reliance on Russian energy, Putin would effectively control or have leverage on all three military and economic superpowers.