Persis, the news isn’t all bad. Two Old Ritualist priests joined the fledgling Russian Catholic Church, and at the Russian Catholic Sobor of 1917, Metropolitan Andrey allowed either the Old Rite or the New (Nikonian) to be used amongst the Russian Catholics, with no admixture of the two. Of these two priests, the first to come into Union (Fr. Evstachy Susalev) came after a personal discernment. Fr. Potapy Emilianov was the second, and most of his parish accompanied him into communion with Rome. His case is being advanced for beatification - the first Old Ritualist Greek Catholic to be considered for beatification.
There are some very attractive spiritual beauties about the Old Ritualists/Old Believers. I myself considered joining the community in Nikolaevsk many years ago while still single, but could not reconcile some things spiritually, especially in light of Vladimir Soloviev.
While no Greek Catholic priest currently offers the pre-Nikonian Russian Liturgy, it is still on the books as a fully approved liturgical usage according to the 1917 Sobor. There are a couple of priests and at probably a couple of deacons in the UGCC that would offer one if the interest were shown and a capable choir found, as the pre-Nikonian Liturgy relies primarily on Znamenny chant and a competent dyachok is needed.
Actually there are aspects of the Ukrainian Catholic liturgical practice that are relics of pre-Nikonian usage, as the Union happened before the reforms of Patriarch Nikon were thrusted on the Russian Church. And even some cultural traditions, such as the wearing of the sorochka (Ukrainian equivalent of the rubashka) and poyas (belt) are sometimes similar. Since both the Ukrainian Greek Catholics and the Old Ritualists suffered terribly under both Tsarist and Communist oppression, there are certain bonds of natural shared experience we have. The relations between the UGCC hierarchy and the Bela Krinitsa group in Bukovina are cordial.
Regarding the Old Calendarists, that is another matter entirely. Since they do not consider even most “canonical” Orthodox to be Orthodox, they consider all Catholics (Greek or Latin or other Easterns) to be heretics and that is that.
My understanding of the arrangement with the UAOC was not that there was necessarily any close relationship, but the “True Russian Orthodox” hierarchy wanted to establish/re-establish legitimate apostolic succesion (as the UAOC did itself with Metropolitan +Dionisy). The UAOC is very friendly with the UGCC, even to the point of having joint services outside of the Divine Liturgy such as Molebens, Akafysts and Panakhydas. Our priests and monks have even been asked to give spiritual talks to their clergy and vice versa.