Most likely some other country (or countries) would simply fulfill the same role of projecting their military and economic power onto the rest of the world to maintain their hegemony. We see this in limited ways already with many other countries, though with a few exceptions, they’re careful in how much they conflict with US interests. One of these, likely China, would move into that role and while the details would be different in some ways, many of the overall dynamics would be similar.
Chinese foreign policy has been fairly cautious and covert compared to other world powers. I think this has generally been a good strategy as it has avoided major conflicts with the US and Europe in recent times.
I can’t think of any coup they’ve directly supported but they certainly have supported military movements and governments in other countries, including Vietnam, North Korea, Myanmar, and Venezuela. So they’ve been a bit less prone to overthrowing governments but they aren’t afraid to use similar tactics to keep friendly regimes in power, and help those factions expand power. So is it a coup to help the North Vietnamese conquer the South? I guess it depends on the definition of coup which can be a fraught word.
Personally I’m not sure I see any of these as coups. The closest might be Myanmar but while China has protected and supported the junta there, it’s not totally clear they actually supported the coup itself. I interpret their actions as seeking stability and wanting to minimize Western influence.
China's foreign policy model seems focused on making deals with the existing power no matter what. Part of that seems to be that China does not believe in odious debt like a lot of Western countries do. When settling debts, Chinese institutions have been far more insistent on keeping write-offs from occuring.
China has also generally pushed for more one on one transactional deals with countries. There have been some international institutions made like the AIIB, but I don't see the institutional creation of systems like the USA tried to do.
A lot of times, the IMF will lead all creditors of a country to restructure, reduce, or reschedule existing debt. What is happening is that Chinese institutions appears to be less willing to write down bad debt, holding up a lot of negotiations between debt holders. So, the debt doesn't get reduced.