There probably is a tactical advantage from the Russian side to putting out the idea that Putin has gone crazy.
Or he really has gone crazy. We can't really know but the fog of war spreading to social media does not seem like a great development.
What other explanation is there for invading a European country with close ties to the USA and NATO -- one claim for the invasion is that Putin was worried that Ukraine would join NATO, if they are that friendly to NATO, then he must have known that NATO would help fight.
Putin thought he would win quickly, get troops to lay down arms and overthrow the government. For whatever reason he was wrong, it seems clear this is what was expected but pushback has been more effective. Probably in no small way because organizing the logistics of such a large operation is hard and has not gone smoothly.
This https://www.youtube.com/watch?v=aZLhRP01jz8 seems like a possibility.
> one claim for the invasion is that Putin was worried that Ukraine would join NATO, if they are that friendly to NATO, then he must have known that NATO would help fight.
Well, look at what's happened. Look at what has happened previously in Crimea, look what happened in the Ukraine separatist regions before. Look at what is happening now. He would not necessarily have to be totally irrational to believe objectives could be achieved there.