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It’s just handled differently now. The hotter part of the conflict in Korea already happened. Its namely just saber rattling at this point, propaganda/influence is a import aspect and necessary tool used by all Empires. “Hearts and Mind” initiatives help keep things in line. A good example of this is for every negative thing said about North Korea on our side of things, there’s a positive thing said about it on China’s side. Both sides of Korea are heavily locked into their respective regimes of the Empires over them.
There is a political and economic rivalry between
China and the US which in some ways resembles the Cold War, in other ways it is more like the pre-ww1 great power rivalries. I don’t see any evidence that a hot war in likely in the near to medium term unless us politicians really wanted it to happen >

We are each other's biggest trading partners. Never going to let war upset the apple cart. >

There is, however, efforts on both sides to weaken that trade reliance though.
China wants to open up more of the world (especially Africa) to its markets, and the US wants to become less dependent on Chinese products.
But, we're going to probably remain too intertwined to go to war any time in the next 50-100 years. >

Nations do irrational things in times of crisis. I doubt a hotwar is coming aswell, however the CCP has been leaning on nationalism to maintain control over their population for a long while now and I imagine sooner or later they're going to be forced to demonstrate action to support their rhetoric. We saw that China was gearing up for a campaign against Taiwaan, I wonder what the new strategy will be now that those ambitions have been squashed. >

For better or for worse, our economic interdependence will prevent us from getting into a Soviet-style Cold war in the near future. All bets are off if we decouple and the world goes multi-polar. China has their 2049 plan of, essentially, supplanting the US as the world's military and economic hegemon. So they're quite open about playing a long game. >

Can there be a cold war without at least proxy military conflicts? The term was developed specifically to characterize the US/Soviet rivalry and it seems like the word war wouldn't have been part of it if it was just propaganda and economic competition, but also involved arming and training military forces in other countries for proxy wars. >

Valid point. Empires doing what Empires do does not  necessarily mean a Cold War. Take into to mind we have a proxy situation in Korea. North Korea is supported by China, South Korea is supported by USA. >

Very good point about Korea and that conflict has been hotter recently but as far as I know it hasn't approached anything like the US/Soviet supported conflicts of the Cold War.