I think that Biden and the war-analysts in the US have planned for all contingencies and are not overly surprised at this next patch of blether from Putin.
No one can control him, but China, to some degree India and Saudi Arabia, perhaps others, and in a backhanded way the US can influence him. I suspect up to a point the US are 'managing' this particular way that things have gone.
I don't think anyone can give you a guarentee that nuclear war won't break out. But I do think very clever people have worked a great deal of overtime to think of ways to minimize the chances.
Lawrence Freedman, one of the most respected war analysts, says:
There is no evidence for now that weapons are being moved into position or being prepared for such strikes. US intelligence, which has been extraordinarily precise so far can be expected to pick up any details (or at least the Russian would need to assume that).
That could change but the profound taboo against using nuclear weopons would have extreme consequences for him - I think it would turn the whole world against him.