Putin's declaration is for local consumption. The Russian public was onboard for a quick operation to protect the Dombas region from the government of Kyiv. Many consider that government to be both under influence of neo-nazis in Ukraine and to be led by a puppet of the US. And either way Russians want their "brothers" to be protected.
Now that it is clear Putin went far beyond the regions that he had the mandate to protect, he has to justify the war, and the only plausible justification is "Russia is under threat". And when you are under threat you get the Nukes ready. He intends to divert the Russian public from discussing the unlawful invasion of Ukraine and the sanctions that will hurt them massively. So he has to make them focus on the "existential threat to the Russian nation posed by the evil West".