From a strategic perspective, Putin wouldn't be well served using Nuclear weapons in this conflict.
Right now the front lines are in territory he claims he's annexed. So he'd be nuking "Russian" territory within a few kilometres of real Russia. He'd be nuking people he claims are his.
If he uses it as a terror tool, like levelling Kyiv, any hope of claiming Ukraine will be lost.
Also dropping a Nuke in Eastern Europe certainly can be construed as an attack on NATO member states as Nuclear fallout isn't isolated.