I’m curious if anyone knows what the official languages are of the other 22 Catholic Churches faithful to Rome.
Latin is the official language of record for all of the Eastern Churches, regardless of which liturgical language they use.
As for official working languages, it is, like in the West, whichever vernacular language is most convenient. Their canon law is in Latin, which is their official language of record.
Significant official pronouncements are composed in the vernacular, and translated into Latin by Church Latinists for record keeping purposes. The Latin translation is the official reference version from which translations into other languages are made.
Just like in the West. Encyclicals and the like haven’t been composed in Latin for quite some time. Few, if any, Cardinals know Latin well enough to write something at the level of an Encyclical, and that was also the case well before Vatican II.
When Pope Benedict was resigning, he wanted to announce his resignation in Latin. He had a Vatican Latinist compose his announcement. At the conclave that elected Pope Benedict, there was only a single Cardinal that could actually speak Latin with any fluency. I think he was from Lativia or Estonia.
For a particularly gruesome example of what knowledge of Latin was among churchmen prior to Vatican II, listen to Cardinal Cushing at the funeral of John F. Kennedy on Youtube. It’s cringe worthy. First year high school at best, and nowhere near the top of his class.
That’s not to knock Cardinal Cushing, but to illustrate that he had only so many hours in the day, and did not consider improving his knowledge of Latin a wise investment of his time. He had bigger fish to fry.