> how they managed to fall so low
I'm amazed that in so many English discussions about China's fall since the 17th century, there are absolutely zero mentions of the Manchus. On the other hand, read any Chinese discussion on it and you'll always see the Manchu domination popping up as a reason if not one of the main causes.
The Manchus took advantage of internal strife within the Ming dynasty during the 17th century and conquered China after the last Ming emperor killed himself when rebels surrounded the palace and a Ming general let them through the Great Wall.
The problem with the Manchus is that they were semi agrarian/semi nomadic and had very little desire for technological progress. Unlike the Han Chinese who always had to frequently rely on technology to overcome the nomads on horseback from the North, the Manchus only believed in horseback and arrows. In fact the late Ming had more natively produced cannons than the Qing dynasty had during the opium wars hundreds years after. Even the western expansion wars conducted by the Qing dynasty early on had gunpowder teams that were only staffed by the Han Chinese because the Manchus initially looked down on guns and cannons.
Lastly the administration was sclerotic because a minority group of 1% was supreme over the other 99%. The Manchus/Mongols/Tibetans owned most of the land in China during the Qing dynasty even though they were a tiny minority. The Manchu/Mongol/Tibetan officials were also of higher status than the Han Chinese. During imperial court, the Qing dynasty had two sessions. After the first one, the Han Chinese had to leave because they were not trusted. In fact up until the late Qing dynasty when the Qing dynasty was ravaged by foreign powers, senior court officials even mentioned to give China to its friends (Europeans/Japanese) rather than give it back to their slaves (the Han Chinese).
This is not to say the Manchus were the only reason for China's downfall (in fact the Ming had started to stagnate a little), but they were absolutely a very large part of it. What many non-Chinese think about Chinese today are actually from the Manchus. The Qipao, the pigtail (Manchu Queue), etc.