Uhh... the USSR occupied the North until Kim Il-Sung took control. Just like the US with the South.
The (current) relationships between the North and China and between the South and the US are very similar, except the US has military bases in the South. But the US does that with all its allies.
As for the ROK military being directly subservient... I'm not as knowledgeable about this, but I think that's only half true. The Korean military largely focuses on logistics and raw manpower, plus their special forces. (Holy shit, Korean special forces are fucking terrifying.) It's largely understood that the US would lead operations, given that the US has more veterans, mass, and better-tested doctrine. However, as I understand, legally, Korea still controls its own military. KOTRA is one exception, but that's a small subset of Korea's military. But to be clear, this is my understanding from passive learning. I could be wrong about things and don't have the time to read up right this moment. I'd appreciate corrections with sources.
Not gonna convince you, but in case others read...
Puppet government is a stretch and depends on your definition. Considering that Ukraine is not a member of NATO despite several economic ties with the US, I don't think it's much of a puppet state, if at all. (Edit: I say this not to suggest that NATO is subject to the US, but it would be highly beneficial to the US if Ukraine had become a member long, long ago.) The Ukrainian government being full of Nazis is generally considered fake news, but I haven't seen evidence one way or the other.
NATO is not imperialist, as it does not establish hierarchical relationships. It is quite egalitarian. If anything, it encourages Europe to be more self sufficient, as the US wanted to minimize commitment to joining a European war. It is also meant to discourage and if possible prevent conflict among members. You could argue post-colonial economic dependence on the US, but... what countries don't have that?
Also, to break the logic in the commenter's argument... if a nation exhibiting Nazi behavior - that is, genocide or subjugation/mistreatment of a demographic under the government's rule - then we should invade the following countries for the mentioned populations:
While I'm a fan of... you know, not abusing populations, I'm also not a fan of invading sovereign nations. So Russia's justification for invasion is a pretense and has a huge amount of historical context around it. OP's argument is highly flawed.
I'll only respond to items with cited evidence. Cited evidence should not include state-backed media or unreputable sources like some clearly extremist "news" site or individual blog.
If you'd like my citations, lemme know. Typed this up on mobile, so a bit of a pain. Corrections always welcome with proper evidence. Being corrected is good learning :)