> Ukraine has crossed many of Putin's red lines, and all that happened was Putin
Ukraine can cross as many of Putin's "red lines" as they wish. Ukraine did not start this war.
Sure, but that's irrelevant to the question at hand. In a discussion of cold game theory, morality doesn't apply. I'd even say that explicitly excluding morality from the discussion is much of the point of boiling a scenario down to game theory in the first place.
The game theory works roughly like this: Putin wins the most if his threats work. If they don't work, he has the choice between drawing a new red line, launching a limited nuclear attack on Ukraine, or full-on nuclear war. The last option is obviously out (guaranteed destruction is in no proportion to the reward). A limited nuclear attack would likely make him a pariah on the world stage and make it even more difficult to find trading partners. So instead he redraws the line.
If he ever went for the limited nuclear attack option Ukraine might give up, and the west would have to choose between war against Russia (high risk, low reward) or just tightening economic sanctions to the max and punishing anyone who dares to trade with him.
If we assume rational actors I don't see how this would ever escalate to nuclear war. And as long as Ukraine doesn't find a way to decisively push Russian troops out Russia has no incentive to climb the escalation ladder. Even as prolonged war leads to internal instability