This is really cool. Both the ultra-monarchist world and the hypothetical ultra-republican world seem very interesting. I must note that I don't think monarchism or even anti-republicanism is by definition bad (and indeed, there is clear criticism of 'ultras' even in the monarchist world; I'd like to know what the place is like). On the other hand, it's kind of funny that the in-universe mapmaker considers his scenario to be evidently evil and scary. Assuming for the moment that the revolutionaries didn't go full Robespierre, the idea of those independent Scottish and Irish states (the latter even nicely confederal, yay) seems rather attractive...
My initial thoughts are that constitutional monarchy is considered the standard. A strong figurehead is considered necessary, though elections are important as well. Ultraroyalists are in favor of strong state churches, weakened legislatures, and more active monarchs. They are generally disliked by the center and left, and are somewhat comparable to a long-standing alt-right.
Regarding the democracy world, Orientoalleghenia It is about as aristocratic as the OTL US at the same time, though more expansionist and active in world affairs, and out to destroy monarchy. To someone who believes England and English-descended settlers should dominate most of the world, having groups active opposed to the monarchy in control is a terrifying thought. I haven’t made up my mind entirely on it, but my gut feeling is that the European states will be rather moderate, at least compared to OTL France at the height of its revolutionary excesses.
So it's from Monarchy World?
No. I don’t exactly know what Monarchy World is, but it is from a similar timeline, assuming that’s a world where monarchism remains dominant.