Or maybe the lesson to Russia is that if the US can't win against Iran how is it going to win against Ukraine? Another angle to look at it is through who does China support (Russia and Iran?).

I think your perspective is interesting and not wrong. The weakness of the US (and the west) is emboldening Putin. I do still think the order of events starts with Russia, China and Iran's challenge the post USSR collapse status quo. In a parallel universe if Russia was able to embrace democracy and become a free country, and if China kept opening up and didn't reverse course, then we wouldn't have the Iran war at all (likely the regime in Iran would have long fallen). The world seemed to be on a course to more freedom, democracy, and prosperity, and less wars, when the Berlin wall fell. And then at some point we went backwards.

As to Putin and Russia it doesn't seem like he has a path to anything that looks like a win. How long he's going to persist is a good question. What is Iran's path forward here is also far from clear. I wouldn't want their sort of "win" myself. It's like Afghanistan's win against Russia maybe. None of these wars have a conclusive win so hopefully a lesson there (to China?) is to think twice before going to another war. Though those lessons seem to be forgotten too quickly.