Thanks to Vegeta and karde, that already helps a lot.
I have also done some research on Dark Ages kindred organization myself, and I think I get it now, and that what I seek is actually very achieveable. I will probably roleplay things this way either way, but I would still like to know if I understand things correctly.
Basically, the core unit of social organization among kindred is the city (or sometimes something comparable, like a small region or tribe or the like). Ultimately, nothing else matters in the Dark Ages, since travel and communication take so much time. The basic template here is very Camarilla-esque, with a Prince ruling over a court and the city's vampire population on the basis of the Traditions, handing out court offices, and so on. The Prince wants to keep order in their city, but kindred may come in from all over and want to settle. So such a court already often involves vampires from multiple clans, and some most likely dwell in the city in either case. What's considered High or Low Clan varies from court to court, with High Clan vampires always being welcome at court by virtue of their clan alone, while Low Clan vampires can still manage to make it to good standing on an individual, just not clan-wide level there. What would later become the Camarilla/Anarch/Sabbat conflict is often already playing out in these courts on a much smaller scale to varying levels, the vampires are just a couple centuries too early to know it.
My impression is that the large, single clan dominated realms like the Courts of Love are not actually (usually/globally) exterminating any vamp not of their clan on sight. That would be foolish. They might, all for the sake of aesthetics and familiarity, provoke the wrath of some powerful sire by cutting off their favorite childe's head. Neither do they truly, absolutely, tyrannize local vampires not of their clan. A sufficiently powerful local vampire of a different clan can still simply force the Prince to acknowledge and cooperate with them. And if you bully a clan too much, they will possibly call on more powerful outside clanmates for help.
So in reality, these realms still use the same basic heterogeneous Prince/court system. They just hoard the power within their own clan and make it harder for the others to gain a foothold. I suppose they might banish non-clanmate vampires, but more likely, their local culture and power system just is unattractive to these and tends to make them seek their fortune elsewhere. Unlike serfs, vampires are probably not globally prevented from leaving by their Prince. THAT is why these realms tend to be more homogeneous relatively speaking, but rarely to 100%.
In that light, for the more mono-clan regions, I kind of the like the idea of playing a slightly more enlightened Prince who values clan culture over clan lineage, and makes a slightly sect-like thing out of it. For instance, a Toreador who considers their clan the greatest and meant to rule, but is still determined to teach the other clans under their rule how to be fancy and will welcome/favor those who are sufficiently gifted at it, though not necessarily on even footing.
Now, with cities being the core of all kindred realms, I see three ways large realms could come to be, and how that would fit CK3's very hierarchical system:
1. Coalitions: Princes of different cities may ally/cooperate, each voluntarily and for their own benefit. Most likely among clanmates, but can theoretically be built upon Roads or individual friendships and the like too. Rather than an absolute monarch, this would make the realm-wide top liege a sort of "chairperson" or "first among equals", and many such realms do have Feudal Elective for their primary titles.
2. Individual dominance: The Prince of a single city holds such overwhelming power as to have other Princes in their pocket. For instance, they may send a loyal childe of theirs to take over and rule another city, persuade/befriend/seduce/bribe/manipulate/blood-bond a Prince, or simply cowe/intimidate/blackmail them into obedience. Factually, this makes them "Super-Princes" of sorts, even though their rank may not necessarily be higher officially. Insanely powerful Super-Princes may do this to other Super-Princes, elevating them to Super-Super-Princes, if you will.
Kindred society is significantly more meritocratic than its mortal counterpart of the time. Vampires do not have a meaningful "Divine Right of Kings" and few will swear themselves to a ruler based just on that. Neither are they primarily guided by ideas of loyalty to a country or nation-state. This may be the Lasombra in me talking, but everything in kindred society stands or falls almost entirely depending on factors such as power, fulfillment of self-interest, networking, convenience, practicality, etc. Vampires decide allegiances out of pragmatism, survival instinct, and chance for gain.
3. Prototypical Sects: Probably built out of either of the above two, or a mix. Notably, neither the Camarilla nor the Sabbat have ranks beyond the city-ruler which are justified by an individual's power/entitlement to rule. Officially, it's based on bureaucracy and practical necessity, like how the higher Sabbat ranks are meant to be a sort of "military high command". So a Sect is simply created when either of the two above realm types manages to enforce a more formalized structure and way of doing things, and it takes hold.
Is this about right?
Also, a semi-related question regarding the mod: Since High and Low Clans apparently diverge regionally, maybe in a future version, you could determine this on a realm by realm basis for each individual clan? Kind of reminds me of the Elder Kings mod and how it lets you choose for each of the major deities whether or not they are part of your pantheon when creating a new faith.