There isn’t any doubt that Putin wants to use Ukraine as a wedge to divide and dissolve both the EU and NATO. He is unlikely to succeed, however, because neither NATO nor the EU has any treaty obligations to Ukraine. He is more likely to unite the two than to divide them, since they are not going to be asked to do a whole lot to deter him.
No, in order to accomplish his objectives, Putin is going to have to be willing to use his Ukraine pressure tactics on a vulnerable EU/NATO member. That could be Poland, but a Baltic state is a more likely target.
To generate a direct conflict with a NATO member would risk escalation and a war that could destroy both Putin and Russia. Is that a gamble he is willing to take?
Let’s hope we never find out.