It is clear at the moment that no Western countries will send troops to Ukraine or set up a non-fly zone in Ukraine because they worry that will lead to a WWIII.

But Putin already said Western sanctions are akin to declaration of war. If Western countries keep adding harsh economic sanctions on Russia, which will destroy the economy of Russia (and Putin's administration hopefully) eventually, there is a possibility that they push Russia to a corner for no choice but fighting back with something and that something could be nuclear weapons.

What is the basis for the Western leaders to believe that emphasizing on harsh sanctions will not lead to a nuclear war with Russia eventually?