If we wanna be nitpicky then autocephaly should be granted by the Patriarch of Constantinople as the primus inter pares of the Orthodox Communion. Although, I would contend that should the Pentarchy be reconstituted that the Bishop of Rome should be given the first among equals designation as the Vicar of Peter. The Primacy of the Bishop of Rome was not the biggest issue which constituted the schism, but Papal Supremacy.
Yeah, my court chaplain is the Orthodox Patriarch of Rome, partly for role-playing reasons and partly for powergamey ones. (The historical emperor deliberately picked a mediocrity to be Ecumenical Patriarch, and his in-game stats reflect this.) It would be very possible to have the Ecumenical Patriarch demand the bishopric of Rome, by event or decision, and hand off that of Constantinople, or for there to be a decision for the emperor to transfer the Ecumenical Patriarchate to the Bishop of Rome, also naming him spiritual head of the Empire. But I can see an argument for the way it is: the Eastern Roman Emperors wanted, for very pragmatic reasons, to make the most powerful bishop in the Church be the one in their capital, not one who lived too far overseas to keep a close eye on, and between the fourth and ninth centuries, you see the bishops of Constantinople coming up with increasingly detailed justifications for why their originally-minor office should be more important than the three original patriarchates of Rome, Alexandria and Antioch.
Autocephalous national churches were common enough that I think the way it works now is an acceptable simplification. Essentially, if the king and his bishops tell Constantinople that they’ve gone autocephalous, it’s a fait accompli.
As for how it works in game: In a quick test game, forming the Kingdom of Syria within the Empire as Duke of Antioch, and then naming either the Patriarch of Antioch or another bishop as court chaplain, did
not create an autocephalous patriarch, which is as it should be. However, as emperor, naming anyone but a patriarch, any patriarch, as court chaplain
does create an autocephalous patriarch for the Byzantine Empire, which is bizarre. It could, however, be a way around the following problem: you also don’t count as having the same religious head as a part of your own empire that follows the Patriarch of Antioch, even if the patriarch is also your direct vassal. (I’ve not tried giving the Ecumenical Patriarch both dioceses, but this really shouln’t be possible.) If the reunited Roman Empire moves its capital back to Rome, I think it might make sense for the Episcopal Patriarchate to move there at well, at least on the death of the current bishop of Constantinople. This could be modded as an event that fires if a new bishop of Constantinople is invested while the capital is in Rome, Antioch or Alexandria.
A test game shows that, if I play as an Abyssinian Monophysite and capture Alexandria, I can grant the Patriarchate of Alexandria to the Coptic Pope, which makes sense. He becomes independent, not my vassal, and is very reluctant to vassalize to me, although I can get him to do it if we have very high relations. Testing shows that, if I appoint my current chaplain patriarch of Alexandria instead, the Coptic Pope will silently replace him and become my vassal, even though I still have an autocephalous patriarch. As far as I can tell, this is hardcoded, undocumented behavior.
Update: In a test game in which I played as the Duke of Antioch, converting to Monothelite and converting the Patriarch of Antioch to the Monothelite faith caused him to immediately abdicate to the Monothelite patriarch. Said patriarch would becaome my vassal if I’d made myself King of Syria by then, but if I were still a duke, he’d vassalize to the Byzantine Emperor instead.
Is this WAD? I’d propose three changes:
1. You should be able to ask any vassal patriarch for a favor
2. If you already have a patriarch of your religion as your vassal, your chaplain does not become an autocephalous patriarch. Arguably less of a problem, because you can always choose to keep your religious head as your direct vassal and name him your court chaplain if you really care. But it’s strange that foreigners would care about his spiritual authority if you don’t, or that the Patriarch of Antioch will accept the spiritual authority of some courtier you pick at random, but not the Ecumenical Patriarch of Constantinople.
3. If there is any patriarch in your independent kingdom or empire, none of it should fall under the spiritual authority of a patriarch outside your realm. (Historically, even before the Great Schism, the Bishop of Constantinople exercised authority over Bysantine Sicily.)