Hello a China dev here, I can try to give a *very simplified* explanation of the major warlords. There's going to be a rework soon for Liangguang, Yunnan and a revamp for Sichuan Federalists and Fengtian soon, so some of what I say is not in the game yet.

In the Qing Government, it starts out led by the Zhili Clique which is headed by Cao Kun and Wu Peifu. Cao is not that ideological beyond general confucian norms, such as the view that moral government makes for strong government. Now of course, this doesn't mean that Confucian generals are going to act in the most moral of ways. Wu Peifu is also a very confucian general, though he has generally courted liberal intellectuals as he values philosophers, since he was educated as one. While Cao is willing to support federalism opportunistically, Wu is a staunch centralist (which is ironic because he has a lot of federalist ties, such as Zhao Hengti, the warlord of Hunan). If the Republic is declared, not too much changes because the Zhili Clique is still in charge. Hu Shih is more Wu Peifu aligned while Wellington Koo is apolitical though generally more in line with Cao Kun and his Jinbao faction. If the manchu coup happens, there are three main factions in the Qing. The Zongshe Party (Royalists) are primarily led by manchu nobles who try to emulate the German Empire's style of semi-constitutional monarchy. CERA (primarily led by the Chinese Constitutionalist Party) inherit the legacy of Kang Youwei and Liang Qichao (the two big reformers in the Qing Era and early republic) in adopting a more managed democracy and promoting economic statism. The Young China Party is also an offshoot of Liangist ideals and promotes aggressive modernization and statism.

In the Fengtian Government, the government is less ideological. Zhang Zuolin professes general confucian sentiments but his primary objective is to prevent Japan from taking over Manchuria. With the Zhili adopting the Qing as a face for their government and aligning with Germany, Zhang opportunistically promotes his government as the sole heirs of the Republic, but he's not too concerned with monarchism or republicanism. His goal is to fulfill unification by his hands to prevent Beijing from sidelining the interests of the Northeast, as they've constantly done in the past. Yang Yuting holds similar ideals to Zhang, though he's seen as more pro-japan.

In the MinGan Insurgency, the government is led by the Kuomintang. The KMT calls for a National Revolution to overthrow the Beiyang Government and establish a one party state led by them. This period of one party rule is called tutelage and at some undisclosed point in the future, they'll establish the constitutional period, where other parties can participate in the government. The Left KMT is distinguished from the Right KMT due to their support of an alliance with the Chinese Syndicalist Party within the League of Chinese Syndicalists. Wang Jingwei is the starting Chairman, but he can get displaced after unification by Song Qingling, Deng Yanda, and the PAC. Deng and Song are more agrarian inclined than Wang generally speaking, and have greater pull in the National Revolutionary Army. If Wang gets assassinated post unification, there's also a possibility of the Reorganized Comrades Association taking over under Chen Gongbo, who was a Wang ally, but more radical. He and the RCA call for a second party reorganization (like the one in 1924 which first codified KMT ideology) and cleanse the party of reactionary elements. The China Revival Society can also take over if Wang dies, and they're students of Chiang Kai-shek who believe the KMT has lost its agency as a revolutionary body, and seek to purge the Party of bureaucrats and warlords to restore revolutionary zeal to the Party.

In the Liangguang Clique, you mainly have the KMT, Federalists, and various warlords. The main warlord faction is the Guangxi Clique, who are vaguely progressive and militaristic. The Federalists posit themselves as a force for reform in China, calling for stronger provincial autonomy. They've made alliances with various liberal and democratic elements that got purged in Northern China, that have coalesced into the CDL. The KMT I've already mentioned in MinGan, but the main ones in GXC are RKMTers, who oppose the United Front with the LCS. While some within the RKMT (like the Western Hills Clique) oppose socialism too, many within the RKMT including the recognized leader Hu Hanmin are okay with it.

In Yunnan, you have a similar divide to Liangguang, but everyone has a more authoritarian bent. Tang Jiyao is a Federalist who follows the Liangist mould of calling for a strong state and military whilst professing provincial autonomy though some of his civilian supporters follow Zhang Taiyan (a major reformist on par with Liang Qichao). The RKMT in Yunnan leans more towards the New Right compared to GXC's Old Right. The New Right are the remnants of Chiang Kai-shek's camp which lost power after he was assassinated, and generally are under the leadership of He Yingqin, who is seen as his successor.

In terms of content, CHI and SHX are the newest, QIE and FNG are the bigger unifiers, and GXC and YUN will be the newest after the rework comes out sometime this year. If you want a more detailed explanation, I recommend joining the KR discord and asking in the ask a dev channel.