> In the absence of US actions, the kleptocrats in Moscow would have been quite content continuing to print money selling natural resources to European industry and then wasting their largess buying up European villas and sports teams. But the siloviki have deep-seated paranoia which isn't entirely baseless (Russia has eaten 3 devastating wars originating from its open western flanks in the past ~120 years).
It is important to stress that the money-oriented kleptocrats and siloviki (KGB-oldtimers) are two opposite groups. Kleptocrats dominated in the 1990s, but lost to KGB oldtimers like Putin, who consolidated power by the late 1990s, because they were more ruthless. In the following decade, they crushed all opposition and turned the country from a dysfunctional democracy into a full dictatorship, and then set their sight on their long-term goal of restoring "the lost empire", which includes roughly 100 million Europeans who regained their freedom when the USSR collapsed. Revanchism has always been at the very core of siloviks.
The countries in Eastern Europe were first to recognize which way the ball was rolling by mid-to-late 1990s, and that's why they set EU and NATO integration as their main foreign policy goals, hoping that tight integration into international organizations would increase their security. Your notion that the US "pushed" NATO enlargement is just plain wrong. Almost the entire Eastern Europe was begging to get into NATO, against very lukewarm reception.
Their completely rational fears were dismissed by existing members with the erroneous belief that Russians were motivated by money, and would not risk harming piggy banks like Gazprom by invading Eastern Europe again. Ironically, that made the eventual entry into NATO easier, as existing members didn't think at the time that Russia posed any real danger. The largest entry took place in 2004, as the NATO was being transformed into an anti-terrorism force in the aftermath of 9/11.
If there's anything to blame the Americans for, then -- according to Andrei Kozyrev, the foreign minister of Russia from 1990 to 1996 -- the Americans could've put more pressure on Russia already in the 1990s to prevent it from declining into a dictatorship. But it was more convenient to remain ignorant of the destruction of Russian democracy and the long downward spiral into a totalitarian dictatorship, and remain seduced by naive illusions like the ones you present us.
For example, the entire idea of Russia as an ally against China is ridiculous. Russians don't care about China one bit and China is not a meaningful part of the public discourse. Russia is a colonial empire run by the city-state of Moscow, with St Petersburg having some historical importance. Take a look at a map. Both St Petersburg and Moscow are few hundred kilometers from the European border. This is where the mental center of Russian government lies, and this is the area where their ambitions are. China, in contrast, is many thousands of kilometers away, and culturally even more distant. China is a strange, faraway place. The Russians who matter (elites in Moscow and St Petersburg) have very little to do with it. Russia does not have a huge outsourced manufacturing in China, nor do they compete in science or technology. Russians are completely outclassed, simple consumers of cheap Chinese goods like most of the world.
Instead, Russians fantasize about the "multipolar world" and other alternative realities where they could be a carbon copy of the US in Europe, but they are in no position to make it a reality. The post-WWII Europe with a hundred million Europeans living under Russian dominance was a historic glitch. Russians cling to this as a mythical "golden era" and are willing to throw everything away in a futile attempt to turn back time. Relations, money, people -- everything. Nothing else matters.
These fantasies are driven by the fact that Russia is a still a feudal society that has not gone through enlightenment. As such, it is incapable of engaging with other European nations on equal terms, in peaceful ways, for mutual benefit. And this has nothing to do with the Americans, NATO, or any other commonly presented excuse. The reasons are purely internal: failure to develop past feudal society, into a modern state, run by professional bureaucracy, guided by laws, adopted by politicians, voted into office by the people, serving the interests of the electorate.