What is Putin’s strategic objective for Russia? I believe it is a “greater Russia” which is strong enough economically and militarily to (a) leverage its natural resources to its economic advantage and (b) play hardball successfully when NATO or its key members try to thwart Putin’s economic aims. “Greater Russia” must therefore include key regions of Ukraine — or perhaps Ukraine entirely — because of Ukraine’s access to the Black Sea and its natural resources (e.g., the Donbas). One way to think of the invasion of Ukraine is as a complement to Russia’s de facto control of Crimea, which is consistent with the “greater Russia” objective.
In view of that, an invasion of Ukraine was almost inevitable. The NATO-Ukraine flirtation made it a certainty. Putin judged — correctly (thus far) — that neither NATO as a whole or the US (perhaps in concert with some other members of NATO) would intervene directly with combat forces. His nuke-rattling is probably an unnecessary bit of breast-beating because US/NATO wouldn’t risk direct combat that might lead to the use of nukes. Putin will resort to tactical nukes (though probably in a limited way) only if (a) he is in danger of failing to secure at least key portions of Ukraine and (b) that failure is clearly (to him) the result of US/NATO assistance to Ukraine (which includes but isn’t limited to intelligence sharing).
If Putin fails, it may well be because Russia’s armed forces aren’t up to the task. But would Putin come to that assessment, or would he blame the US/NATO? I suspect that he would do the latter, which means that intelligence sharing (among other things) is probably a bad thing.
The smart move for US/NATO is twofold. First, continue to lambaste Putin publicly so that his role as the “bad guy” is (mostly) unquestioned in the West. Second, continue to help Ukraine (to do otherwise would be bad p.r. and a overt sign of weakness). But US/NATO would take care to avoid actions that might cause Putin to conclude that he failed because of US/NATO interference. (I don’t suggest that course of action lightly, but a temporary loss is better than a permanent one. I am reminded here of Churchill’s decision not to warn the citizens of Coventry about a massive air raid because doing so probably would have compromised the Ultra program and resulted in a far greater loss of Allied lives in the course of World War II, if not defeat for the Allies.)
By the same token, it is imperative that the US/NATO grow some backbone and let Putin know that what he has in mind for “greater Russia” is matched by NATO’s commitment to the security of its member nations. Letting Putin know means (a) policy declarations to that effect, (b) firm commitments to building up NATO’s military strength (Europe still needs to pull more weight), and the “natural” expansion of NATO to include Finland and Sweden. (Does Putin really want to go to war over the inclusion in NATO of Sweden and Finland? I doubt it. Their admission to NATO would be a clear signal to Putin that he might have a free hand in “greater Russia”, but that’s it.)
In sum, though it pains me to admit it, I’m suggesting something like a new Iron Curtain, where the curtain is (mainly) designed and built by the West. The new status quo would resemble that of the 1950s and 1960s, when the US/NATO declined to interfere in matters behind the original Iron Curtain (e.g., the suppression of the 1956 uprising in Hungary and the “Prague Spring” of 1968). But the new Iron Curtain would be a semipermeable membrane, allowing trade with Russia where it is mutually beneficial. And, with a sufficient show of strength by US/NATO, the new status quo wouldn’t engender constant dread about what Russia might do with its nuclear arsenal.