Obviously Russia would not start a nuclear war. It will simply take steps that either need to be conventionally opposed or dare US/NATO to go nuclear. Sanctions are hoped to collapse the economy of Russia and put the fear into the Chinese and other fence sitters. It's like running the clock down in a game. US probes for incremental steps (the famous "salami slicing") to ramp up counter force. Nothing should happen until we have Russia's promised counter-sanction response this Tuesday. After that next move is getting planes into Ukraine and possibly NFZ. What follows will be a non-nuclear hypersonic attack on NATO airfields used. And so on. Until someone lobs a nuke.
Oh no, that wouldn't be their objective. Which would be rather 1) military (obliterate resistance) and 2) political (show the resolve to use whatever means they deem necessary).
I think the major conclusion from the Ukraine war is that the Russian army is not in a particularly strong condition, and certainly would not fare well against superior NATO forces (particularly the air forces.) And this is assuming they are not further degraded by a long, bloody occupation in Ukraine. Nuclear first-use is a move from weakness, not strength.
Also, keep in mind that Russia is already spreading FUD about Ukrainian dirty bombs (https://www.reuters.com/world/europe/russia-without-evidence...).
All of NATO
NATO have been quite clear that the line is attacking a NATO member. Russia is pushing that line by invading a country they believed was about to join NATO, but they have not yet attacked a NATO country
I'm not saying I know the answer. But this is what strategists on the US/NATO side would be thinking about, and Russia sure knows they would be thinking about it. It would be madness to gamble on this strategy working out in the long run.