Sanctions put pressure on Putin, but were not strong enough to force him to back down. Russia has had first-hand experience with sanctions when they invaded Crimea, so they were expecting this and took it into account. What would have made Putin stop was a treaty with NATO but that's a bit too late now, is it? If the US doesn't have any ill intentions against Russia, then it's very easy for them to say "no, we're not going to make Ukraine an ally" because Ukraine doesn't qualify anyway. And since it's a treaty, the US could have made counter demands like "they would only agree if Russia promises never to invade any country again." But they didn't, proving all of Putin's claims in the face of the world. Yet the rest of the world decided to join the US in sanctioning Russia anyway, which they've never done when the US invaded Afghanistan for a fabricated claim. But Russia will survive the sanction and the countries that sanctioned it will be the true losers of this war because they've lost a lot but didn't gain anything. Ukraine is still gripped by war.
You have described the problem very well. All the world's media are shouting that the war started because Putin wants to conquer Ukraine and take it for himself, but no one remembers that for several years he asked the West to refuse to join Ukraine in NATO, not to interfere in Russia's affairs. In the end, how did.
Ok, let's assume you're right.
Then a couple of simple questions:
1. When did Ukraine officially decide to join NATO?
2. Before that, were there NATO countries bordering Russia? If so, do they pose a threat to Russia? And why is Ukraine more dangerous for Russia?
3. What happened before - the event of the annexation of the Crimea and part of the eastern regions, or Ukraine's statement about the desire to join NATO?