That's never been a long term strategy of NATO. It's ridiculous on its face. "Encircle"? Just take a look at a map - Russia stretches all the way to the Pacific. It's border is nearly 36,000 miles long, and most of that doesn't even border on NATO. How the hell could NATO possibly "encircle" Russia?
"Strangle"? The exact opposite was happening for the past 30 as Russia's economy was becoming more integrated with that of the rest of Europe, especially in terms of energy. Prior to Russia deciding to invade Ukraine and set off sanctions, where was there any effort to "strangle" Russia? And why would anyone have any interest in that?
And "subjugate"? Seriously? What actions did NATO ever take to "subjugate" Russia? Nobody had or even has a shred of interest in conquering Russia. If Putin truly would have feared that, he would never have invaded Ukraine and risk NATO intervention at all. The only reason he invaded was because he was sure that NATO would not start a war, which is the exact opposite of what you'd expect from an alliance whose goal was to "subjugate" Russia.
You've bought a bunch of Russia propaganda hook, line, and sinker.
NATO is a military alliance that outlived its purpose since the Warsaw Pact dissolved; it has steadily expanded to Russia’s borders and even instigated a 2014 coup in Ukraine and installed an anti-Russian government. Only 300 miles separates the Ukrainian border from Moscow itself, and now Russia has decided to invoke its own Monroe Doctrine. Many of us saw this coming twenty years ago.