If China wants a war with the US -- which I doubt, seeing as they haven't started one by now and Taiwan would be a better reason for them to do so -- they don't need a treaty to have one. They can just go kick one off. The treaty just means that:
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They have an obligation to act.
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It provides grounds under the UN rules to act legally. But, end of the day, that only really matters to the degree that it affects what other countries do. And in this context, that probably mostly means the US anyway.
If you look at Hong Kong, China just told the UK to get out or they'd take it. They didn't have a legal basis for that. I don't expect that a piece of paper would be a huge obstacle to involving themselves in Korea if they were willing to have a war over it.
https://en.wikipedia.org/wiki/Handover_of_Hong_Kong
During talks with Thatcher, China planned to seize Hong Kong if the negotiations set off unrest in the colony. Thatcher later said that Deng told her bluntly that China could easily take Hong Kong by force, stating that "I could walk in and take the whole lot this afternoon", to which she replied that "there is nothing I could do to stop you, but the eyes of the world would now know what China is like".
There’s a reason they are constantly provoking Filipino ships and the like
I don't think that that indicates a desire for war. China has had outright hostilities over the islands before, with Vietnam, and China didn't aim to convert it into broader war. I think -- though I don't follow the South China Sea situation much -- that China's aim in the South China Sea is to maintain a level of friction high enough that it's painful for the countries to maintain a claim over those islands. At some point, the country either de facto or de jure cedes the territory and China keeps it.
EDIT: There's the Vietnam instance, where they brought friction up to a level of conflict, grabbed de facto control, but didn't initiate a broader war:
https://denvergazette.com/colorado-watch/colorado-parental-evaluator-indicted/article_e24e85f4-810a-11ef-8bf2-23b05d767098.html
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