There are two problems with your reasoning. First, you’re assuming Putin’s use of nukes would make him automatically win the war. That’s not how it works. Second, you’re ignoring other possibilities. For example, an interesting response to Russian attack would be an “unknown party” detonating a dirty bomb in one of Russian cities. It’s easy to do technically, wouldn’t result in large casualties, couldn’t be blamed on NATO, and would require absolutely enormous cleanup effort that would likely topple the regime.
I don’t think or believe Putin will necessarily win the war by escalating to the use of nuclear weapons.
I just think he has been very consistent in “doing what he says, and saying what he does” over the long-term.
And that his personal credibility is tied to this conflict, so escalation is likely.
Escalation by Putin doesn’t guarantee victory(or the semblance of it), but de-escalation by Putin is a guarantee of failure(credibility).
The US has just leaked its unhappiness with Ukraine conducting targeted assassination in Russian territory(seperate from train/logistics sabotage).
But a dirty bomb detonated in Russian territory is far more likely to be a Russian casus belli, akin to Nazi false flag action in Poland in 1939 and Putin/Shoigu false flag action in 1999 with the Moscow Apartment Bombings.
Putin said he won't invade. Then he said Kyiv will fall in three days. Then conducted fake referendums, "annexing" territories he doesn't control. Izyum was declared a part of Russia forever from now on, and that "forever" lasted two days. So, this "doing what he says" doesn't quite check out.
As for casus belli - against whom exactly? And why would Russia need any casus belli?