...
...
On your other points, I hope you're right, but I'm worried that Putin
may actually be mad. I can't see how
any part of this Ukraine invasion is rational from
any perspective.
...
Putin is not mad in the usual sense, he is just falling into a Russian Maximalism and a neo-colonialism. This is a game old as humanity - under the rules of the "Big Game", the invasion of and Ukraine that was looking to tighten the ties with the west and was about to join a different "sphere of influence" allows him to maintain the status quo of Russia, perhaps even to enhance it.
Even with a limited success in the south by capturing Odessa, Mariupol and the access to the Black Sea, he, under his inhuman view, would have achieved a major strategic victory.
The old game... money, ego, power, ... all that brought Europe to WWI and WWII with millions of dead. That how Europe learnt the price of nationalism and despotism and that is why European governments in which people have a say do not want to hear anything about waging war in Europe. This is often confused with weakness, as the democratic rivalry is often confused with chaos.