If I am not mistaken, I believe that the Italo-Albanian Catholic Church also never broke communion. But you are correct, all of the others had.
For the most part the Italo-Albanian church has roots in Orthodox immigrants from Albania.
They came to Italy as refugees after the death of Skanderbeg. The priests they brought with them were Orthodox, originally ordained by Orthodox bishops in a state of schism from Rome.
There may have been some (very few) eastern rite Greek Catholics in Italy, descended from the great church that preceded them on the site, but their bishops had ceased long before and they were regarded as part of the local Roman Catholic establishment, all of the dioceses had been converted to Roman Catholic ones and ordaining bishops (if there were any) would have had to be brought in from outside for several hundred years. It was a church (if one could call it that) with no hierarchy nor synod, no patriarch, and no Sui Iuris rights. (It’s priests would be formed under the care of Roman Catholic bishops in Roman Catholic seminaries.)
This is much like the modern Russian Catholic church in the USA, which exists only as long as the Roman Catholic bishops are willing to support it, with no bishops of it’s own.
There is no evidence I am aware of of the two groups (Albanians of Italy and the earlier Greeks) mixing, although one might assume they did if the earlier population had not already completely converted to the Latin church in some particular locale. For the most part if anything like a ‘church’ survived it did so in
customs and
habits of the local Roman Catholic laity who had Byzantine ancestors. Even Grottaferrata had a liturgy that was so bastardized and Latinized (and accepted local Latin Catholics from it’s territorial parishes) that if it represented anything it would be the sorry state of the small ‘Greek’ remnant.
This is hardly continuity, and the new immigrant church of Albanians had no standing hierarchy in Italy until the 20th century, when a Pope carved out a little piece for them and gave them bishops from his own line. The names for the two dioceses do not reflect anything ‘Greek’ about them, these were established to save the Albanian ethno phyletic remnant, which was fast disappearing. So the official history of the Albanian church in Italy is less than one hundred years old. Anything beyond that is embellished myth.
Today (sadly), that church has no bishops of it’s own. The Pope has not given them any and they do not have a right to name their own. They are under the care of Roman Catholic bishops once again…
… and the Italian synod of bishops has recently reaffirmed that all priests in Italy are to be celibate, I would not expect them to ordain any married men for the ‘Albanians’, and it is unclear how many married men are priests in that very small church even now.