And why must NATO help Ukraine?
Hell, the world doesn't even want to put sanctions into use and the ones they have put are puny visa restrictions and asset freezes, what makes you think that they would wage war?
And why must Russia invade Ukraine?
You are positing a Russia that is acting far more boldly then Russia actually is. Russia isn't going to invade Ukraine because it would be hopelessly outnumbered by even a half-hearted NATO intervention.
I'm with the pessimists here. I see Putin playing the long game, using agents provocateur to stir up trouble in eastern Ukraine and foment separatist activity.
That's not the long game, that's the short game. Russia is never going to have a better opportunity then right now. While it's possible that some unexpected twist will give them a new opening that's the outside bet. It's worth trying for because it costs Russia almost nothing to try but they know it's not likely.
Look at real world insurgencies. The CIA didn't create the Mujahadin out of thin air, they just supplied existing groups. The KGB didn't invest south american left wing revolutions, those predated the Soviet union. Imperial Germany didn't invent the Bolsheviks to destroy the Russian Empire, they just helped them. Astroturf groups have a vanishingly short lifespan before they are exposed as foreign agents. They can be occasionally useful in
briefly creating ambiguity when the world isn't paying attention but
Ukraine is already in the spotlight. The KGB can't quietly cultivate an astroturf group in Ukraine because you can't do covert ops when you aren't covert.
If Kiev stays its hand, you see another highly suspect "referendum" and the region follows the lead of Crimea into Russia's waiting arms.
The Russians can't rig an election they don't control.