This makes European interaction come a lot earlier and more interestingly. Spain will certainly come for God and Gold, as will the Dutch (well more on the Gold) and eventually the Brits and French. I’d imagine it be like India (everyone plays them off against eachother…until there the ones being played off).
In terms of European interference in this timeline, whilst I do think more territory would be hoovered up, what happened in India would be difficult to happen here. This would be a divided China between two very centralised bureaucracies in possession of huge armies, not so much a dynastic implosion and following warlord era as it was with the Mughal Empire.
Mmm, looking at this: I don’t think the Europeans can actually do their divide and conquer game, mainly because you have too compact states, who can resist. In fact, ironically, this may lead to stronger states come the 19th Century. War equals need for better weapons, need for better weapons equals more trade with the west, more trade with the west equals guns (yay) and economic/political development leading to stronger states playing a hand in politics.
Necessity is the mother of all invention after all. They might not quite be able to do what Japan did, but a China that is forced to modernise is still in a far better position.
Generally speaking, I don't quite expect either of the two Chinas to end up like India. Rather, think more of a more pronounced version of what happened to China in OTL-- or yes, indeed, to Japan. (Siam might be another point of comparison.) Of course, we shouldn't over-estimate the Chinese ability to just happily accept European guns & stuff, magically modernise, and then advance easily towards the status of a significant developed power. These things aren't easy, and both Chinas face serious challenges.
Without the conquest of the South, and with the Ming remaining, the Qing lack vital legitimacy. In addition, because they rule less of China, they actually end up making a relatively larger cultural contribution to the Northern realm that they do control. So it'll be easier to paint them as "foreign barbarians" (something that was an issue in OTL, and will be -- roughly speaking -- twice as big an issue in this ATL).
Meanwhile, the Ming have been diplaced from most of their empire, have been forced to abandon their capital, and are now re-constituting a functional state via emergency measures. Something that was
fatally impopular in OTL, and will be survivable but still very risky in the ATL. So they'll have to navigate the needs of retaining popular support and the air of legitimacy, while still ensuring they have the funds and the military support to keep their Northern border secured.
In this context, it is almost inevitable that European interlopers will offer "assistance". Presumably, rival powers will offer it to the two Chinas, respectively. While this will give both Chinese realms access to very useful technology, it will also create a certain economic dependency. Not to mention the fact that the Europeans will no doubt demand political inflyence in return for their... generosity.
Neither will the decline of Spain and Portugal (the likely early players) offer a good chance for the Chinese realms to free themselves from European influence, since France and Britain (joined by various lesser players) will be right there to muscle their way in.
All in all, rather than colonial holdings, I think the two Chinas will be "dominated nations", along the same line as (but to a greater extent than) unified China was in OTL. If there is eventually some equivalent of a Great War and the Chinas stay out of it, that would be an excellent opportunity for them to ensure their future independence. If they are however dragged into it, they may well remain entangled in their respective European-led alliance systems for longer...
I also suspect in this TL, we wouldn’t be talking about the breakup of China. Rather The Ming (who control most of Han China) would just view themselves as the Chinese and the Qing would be viewed as the Manchus. The upper areas is an area for 20th century nationalist fantasies to talk about retaking.
The Ming would certainly paint the Qing as foreign barbarians, but in their own realm, the Qing would go to great pains to present themselves as th legitimate ruling dynasty of China-- denouncing the Ming as degenerate and corrupt figures ruling over a court of
Southern barbarians. (The tendency in Northern China to regard the South as basically barbarian and in Southern China to view the North as barbarian exists even in OTL, to this very day. Nobody really believes it nowadays, but it's still a meme. Historically, to the South, the North was half-Mongol, and to the North, the South was half-Vietnamese.)
Both regimes will have maps claiming all of China for themselves, and marking the rival regime only as "provinces in rebellion"-- if even that. They might just outright pretend to be ruling the whole realm.