But why? We have many examples of war activities between states with nukes.

If tomorrow russia will occupy three NATO countries: Estonia, Lithuania and Latvia - nobody is going to use nukes.

We only have one direct example - Pakistan and India, and nukes came out within hours of the conflict starting, and it was settled rapidly afterwards.

And I do think conflict in the Baltics would leak to nuclear war rapidly. Formal military alliances must be upheld, or they mean nothing. If the positioning of nuclear weapons didn't immediately end the war (as in Pakistan-India) then there would likely be limited launches of tactical weapons at invading forces. At that point we reach the crisis point. Either the war ends there, or we get retaliatory nuclear launches at which point the most likely scenario is the majority of the northern hemisphere becoming a depopulated wasteland.