I think Russia probably can succeed in occupying significant parts of Ukraine, but I think the idea that it will ever succeed in occupying the entire country is much more dubious – especially the westernmost regions, such as Lviv. Far Western Ukraine is the culturally most dissimilar from Russia – being dominated by Ukrainian speakers and with relatively few Russian speakers; having an Eastern Catholic rather than Orthodox majority, and with most of its Orthodox population belonging to the Orthodox Church of Ukraine (OCU) rather than the Moscow-linked Ukrainian Orthodox Church (UOC-MP); a lengthy history of rule by Poland and Austria – all of which makes it a hotbed of Ukrainian nationalism whose population are among the most likely to give sustained resistance to any attempted Russian occupation or rule by a Russian puppet government. Added to that, it is geographically protected by its borders with NATO member states (Poland, Slovakia, Hungary, Romania), which prevents Russia from encircling it, and gives it guaranteed supply lines; and Russia must be wary of fighting near those borders, given the risk that NATO might be drawn into the conflict. Moldova to the south also provides some protection – although Russia could conceivably invade Moldova as well (and indeed already de facto occupies the breakaway Moldovan region of Transnistria), doing so may risk overextension, and given the deep cultural and linguistic links between Romanians and Moldavians, risks drawing Romania (and hence NATO) into the conflict.
I really don't think Russia has fully thought this through. It is conceivable the war may end with a split of Ukraine in two, one internationally recognised but with significantly diminished territory, the other a Russian puppet regime only recognised by Russia and its close allies. It is conceivable the war may end with Russia annexing further large chunks of Ukraine, especially the South and the East and maybe even significant parts of Central Ukraine. It seems very unlikely it will end with Russia, or a pro-Russian regime, controlling the whole of Ukraine.
NATO receives no benefit by standing by and letting Ukraine fall. The next fight would be on NATO soil, against a battle hardened, victory spirited aggressor. Oh, and he would know for a fact his nuclear threat worked like a charm.
Now is the time to stop Russia’s aggression once and for all, nuclear threat or not. Putin has never gotten less crazy. There is zero reason to assume a Ukrainian victory would pacify him. We will win handily against any future conflict. But why choose a harder victory tomorrow with one less ally, when we could have lasting victory today?
If he is rational or not I do not know but there can be a great deal of difference between what he wants to do and what he can do because of resources and capability.
The nuclear threat only takes you so far since it’s understood as a last resort response. Even an irrational actor realizes the minute he unleashes nukes he…and everyone else loses.