Good points you have made. I wasn't suggesting that every decision that Qing China makes is a mistake, but I am simply saying that they have had a knack, historically, for making very terrible decisions. The POD I would choose for this TL would be Yuan Shikai choosing to side with the Qing Dynasty in 1911. This would leave the Qing Dynasty in power, but it would be controlled by Yuan Shikai, who acts as a military dictator with the Qing monarchy as a mere powerless figurehead. Yuan already tried to make himself have complete power over China when he tried to reinstate a Chinese monarchy with the Yao Dynasty in 1915. In this timeline, Yuan is the defacto ruler who essentially has complete and total rule over China except in name only. Now, about the Chinese military: it wasn't completely backwards and it didn't have only 19th century technological weaponry. China underwent lots of military reform following their defeat in the First Sino-Japanese War, leading to them reforming some military units. These units were known as the new army. The most successful of these unites was called the Beiyang Army. China's military, especially the Beiyang Army, had gotten a lot stronger since the First Sino-Japanese War, meaning that, at least from Yuan Shikai's perspective, China is militarily able to engage in a large-scale war. The Chinese army was far stronger in this time period than in 1895. Militarily, at least from China's perspective, they will do well. Because Japan would rush to get Tsingtao earlier due to potential Chinese entry with the Entente, Yuan Shikai's China would know that their military is far more modernized and would be able to survive a large-scale conflict. What do you think would have happened if the Qing entered the war on the side of the Central Powers? I really am curious about the greater Asian involvement in World War I.
Side Note: This is one of my first posts, so please don't be super annoyed if what I'm saying makes no sense.
Welcome to the site!
Certainly, if Yuan backed the Qing in 1911 it makes setting up his dynasty much easier.
But as I said before, there's still a fundamental problem with a POD that late- it doesn't give any reason for China to back the Central Powers. Yuan and his successors didn't try to historically. Why would they now?
If you want greater Asian involvement in WWI, don't look to China- look to the subcontinent. An Indian rising is difficult to engineer, but much more possible than a China that enters the Central Powers. Furthermore, there actually were German efforts at engineering one.
Also, far more than China- a front in India actually has the potential to massively divert British resources, whereas a Chinese front simply wouldn't threaten the Entente. The Russians and Japanese both outmatched the Beiyang Army individually, even during the war. Together, they'd smash it.
Plus, if Yuan was foolish enough to join the Central Powers it would almost certainly lead to a full civil war as the KMT and anyone else who put their hands up got given Japanese and British arms.
I'm not annoyed- as I said, it's a fascinating period for China. But there's nothing wrong with accepting that the original framing of the question may not be helpful. As I said before, if you want the Qing to join the Central Powers and be strong enough to make a difference, you really need a POD in the nineteenth century.
As a very rough handwave- a more successful self-strengthening movement leads to a narrow victory in 1895. Korea still probably leaves the Qing sphere, but the stalemate is seen as the teething pains of a modernising power rather than the revelation that China was a paper tiger.
Consequently, those Britons who believed that China is their natural ally in the region win out. There is no Anglo-Japanese alliance in 1902. The British continue to maintain economic influence, but Japan worries more and more about strategic isolation. With no great power backers, it backs down over the growth of Russian influence and never goes to war with the Czar.
The Qing continue to reform. Corruption remains rampant, but infrastructure is slowly developing. The end of the eight-legged examinations sees the co-option of more and more youthful talent into the bureaucracy- young men who would join the KMT in our timeline become the basis of a generation of modern mandarins. There is more and more tension, however, between the Manchu court and the powerful Han leaders of the civil service and military. Li Hongzhang is an unofficial regent for the first part of the twentieth century, but after he dies it becomes more and more clear that his protege Yuan Shikai wants to exercise power in name as well as practice.
For Korea's part, the next twenty years seem to go well. The newly-minted Empire remains in terror of annexation by one of its three most powerful neighbors, but cautious steps towards building a modern state continue. Korea slowly drifts towards Japan- its reformers caught between fear of becoming a colony and the knowledge that China and Russia are more likely to simply annex them.
Meanwhile, in Europe- because there is no humiliation of 1905, Russia is perceived as far stronger and more dangerous than it is. Germany behaves more cautiously, France more boldly. Franz Ferdinand has an uneventful trip to Sarejevo in 1914.
By 1917, Russia seems poised to overtake the Kaiserreich. It has had a decade of social upheavals, but nothing apparently crippling. There is probably a paper Duma. Britain is worried enough about clashes with Russia in the Straits, Central Asia and the Far East that it backs away from its understandings with the Entente.
Germany has come to believe that if it is to defeat the Entente it must move now. When a crisis breaks out- perhaps a Russian agitator named Trotsky throws a bomb at the funeral of Franz Joseph in Vienna- Berlin makes its move.
Within months, it's war. Germany and Austria-Hungary against Russia and France. Russia seems not to be quite as fearsome as it initially appeared, but compared to OTL the eastern front is a far more close run thing. In the west, France awkwardly batters itself against the Rhineland and Alsace.
In 1918, the French push through to the Rhine. Despite initial setbacks in Poland, Russia is pushing into East Prussia. Faced with the threat of the Czar becoming the master of Europe, the British cabinet issues an ultimatum to the Entente to come to a Conference of London. A week later, the UK joins the Central Powers. It looks for the chance to open new fronts in Russia that don't involve fighting in the highest reaches of Central Asia. One consequence of this is a determined push by London and Berlin to get the Ottoman Empire to join the Central Powers.
The second is that in 1919 the Qing send units to close the Trans-Siberian railroad. Though the Qing-Russian fighting reveals the astounding weakness of both supposedly modernised armies, it also leads to one of the bleakest and most brutal fronts in the history of warfare as large, under equipped forces struggle across a vast and ungoverned terrain.
The tide is turning against the Entente- Russia is now trying to supply fronts on the Baltic, the Caucasus, the Balkans, Central Asia and the Transbaikal. Reluctantly, it agrees to cede all interests in the Korean Peninsular and southern Manchuria in exchange for Japanese (and, nominally, Korean) entry into the war.
As 1920 begins, the alliances are-
The Entente of Russia, Japan, France, Romania, Italy and Korea against the Central Powers of the UK, Germany, Austria-Hungary, the Ottomans, Bulgaria and China.
How it plays out after that... I don't know. Just a few fun thoughts, not a serious attempt at plausibility. There is more handwaving involved than the Queen acknowledging a hundred parades.
As always in the Great War, much comes down to where the Americans jump.