The problem with brinksmanship is that you have to be prepared to go through with the act you threaten and accept the consequences of it. Take Snake Island for example where the response was literally "fuck you". There were only 13 people defending the island yet Russia spent an enormous amount of money to level the place by naval bombardment rather than attacking by landing troops. Because ultimate the threat isn't hollow and the island itself is pretty worthless.

With threats of nuclear weapons it:

- Makes Putin and Russia look weak, they have to threaten literally the worst weapons they have to beat Ukraine.

- Actually using them might cause nuclear retaliation.

- Actually using them is going to absolutely cause an enormous international response and almost certainly remove any allies they have in the US etc.

- Actually using them is going to ruin a portion of the country you want to take owner.

Nuclear brinksmanship is a non-starter.