Re: Which period of Chinese history is most similar to today's geopolitical situation
I don't think there is any deliberate attempt to find historical parallels, but more a case of having the long and rich history of China in mind and making correlations and connections when something jumps out at you.
In that sense, it is less a case of trying to figure out which period the current one resembles the most, since that is forcing the issue, and there is always the danger that you will start to look at things through a prism of preconceptions instead of seeing things clearly for what they care.
History is a rough guide to give you clues, insights and warnings, and there can be a thing as reading too much into history, since every event is singular and have countless different factors and variables that sets it apart from any historical comparison that trying to predict an outcome based on history is more art than science. The mere fact that something similar has happened in the past will on its own alter the way current and future people would deal with an event if they knew of that historical example.
In the broadest sense, in terms of top end geopolitical contests, you could argue that the current world order is similar to the 3 Kingdoms period, with one dominant power (America and NATO, with America like Cao Cao, assuming the powers of the Emperor to command the Imperial forces [NATO]) and two smaller powers who would often unite to try to counter it (China and Russia).
In a way, it is hard to find appropriate parallels because there are so few times/instances when China was the underdog. Even in dynasties where a foreign forces has invaded China, they are always considered to be backwards barbarians who only managed to take over China because of internal Chinese strife and weakness.
As such, it might be more appropriate, interesting and assuming to see which Chinese Dynasty and period the current America most resembles, while modern China plays the part of the upstart barbarians.
I will get the ball rolling and suggest that modern day America is very similar to mid-late Ming, which modern day China is like the Manchu.
Just as the Manchu coveted the wealth and status of the Ming, so China covets the wealth and status of America. The Manchu studied Chinese technology, and even adopted much of Chinese culture and language as their own in their bid to overthrown the Ming, modern Chinese are eagerly learning western, largely American, skills and technology and English and American popular culture is taking ever stronger hold in Chinese society through compulsory English lessons, Hollywood TV and films and now also increasing through studying and traveling in Europe and America.
I think that just as the Manchu were permanently changed by their interaction and overthrow of the Ming to become more and more like the culture they overthrew, so modern China will become more and more like America as a natural consequence of China's attempts to catch up with America through emulation. Although I do not think modern China will change as much as the Manchus did to become like the culture they overtook. For one thing, I don't think China will ever take over America physically like the Manchus did China, and the Chinese are too convinced of the inherent superiority of their own culture to wholesale abandon it and adopt someone else's.