Deacon Paul,
You are correct. The Churches which decidely are of Ruthenian heritage - the two denominated as Ruthenian (Pittsburgh and Mukachevo), the Slovak, and the Magyar/Hungarian Catholic are, by virtue of being 'sui iuris', distinct from one another. The same is true of the UGCC which, despite having its own 'heritage', serves according to the Ruthenian Rescension and, therefore, could be classed with the others on that basis.
Thus, 'commmunion' among them, in a very narrow sense, is solely by virtue of their being of the greater Catholic Communion. They have no formal canonical, administrative, or hierarchical ties to one another in the nature of an authoritative format nor do they have any standing structure in which they interact on matters that commonly relate to the lot of them - e.g., liturgy.
That same problem afflicts several other Churches as well - all of them Byzantine. (The exception being the Italo-Graeco-Albanians whose three hierarchs have met on several occasions to discuss and address mutual issues/concerns.)
The full breakdown of Churches
sui iuris in the Catholic Communion actually totals out to half more than the 22 commonly cited, because the 'stand-alone' status of a number of jurisdictions (putting aside the theoretically stand-alone status of jurisdictions in the diaspora and, thus, outside the 'historic territories') effectively inflates the number.
Patriarchal:
1. Armenian Catholic Church
2. Chaldean (Assyro-Chaldean Catholic) Church
3. Coptic Catholic Church
4. Maronite Church
5. Melkite (Byzantine) Greek-Catholic Church
6. Syriac Catholic Church
Major Archeparchial:
7. Romanian (Byzantine) Greek-Catholic Church
8. Syro-Malabarese Church
9. Syro-Malankara Catholic Church
10. Ukrainian (Byzantine) Greek-Catholic Church
Metropolitan:
11. Ethiopian (& Eritrean) Catholic Church
12. Byzantine Ruthenian Church (US)
13. Knanaite (Syro-Malabarese) Catholics (Metropolitan Archeparchy of Kottayam of the Knanaites)*
14. Slovak (Byzantine) Greek-Catholic Church
Eparchial:
15. Bulgarian Byzantine Catholic Church (currently, functioning as an Apostolic Exarchate)
16. Croatian (Byzantine) Greek-Catholic Church (Kriveci)
17. Croatian (Byzantine) Greek-Catholic Church (Serbia & Montenegro) (currently, functioning as an Exarchate)
18. Greek Byzantine Catholic Church (Constantinople) (currently, functioning as an Exarchate under Apostolic Administration)
19. Greek Byzantine Catholic Church (Greece) (currently, functioning as an Exarchate)
20. Hungarian (Byzantine) Greek-Catholic Church (Hajdudorog)
21. Hungarian (Byzantine) Greek-Catholic Church (Miskolc) (currently, functioning as an Exarchate)
22. Italo-Greaco-Albanian Byzantine Catholic Church (Eparchy of Lungro
degli Italo-Albanesi in Calabria)
23. Italo-Greaco-Albanian Byzantine Catholic Church (Eparchy of Piana in Sicily
degli Albenisi)
24. Ruthenian (Byzantine) Greek-Catholic Church (Mukacevo)
Eparchial - currently
sine episcopi:
25. Albanian (Byzantine) Greek-Catholic Church (currently, functioning under an Apostolic Administrator who is, himself, Byzantine but not of the Albanian GC Church)
26. Belarusian (Byzantine) Greek-Catholic Church (Belarus) (currently, functioning under an Apostolic Visitator
ad nutum Sanctae Sedis)
27. Belarusian (Byzantine) Greek-Catholic Church (UK) (currently, functioning under an Apostolic Visitator
ad nutum Sanctae Sedis)**
Exarchial (never having been elevated to eparchial status):
28. Italo-Graeco-Albanian Byzantine Catholic Church (Exarchic Abbey & Territorial Monastery
sui iuris of Santa Maria di Grottaferrata
degli Italo-Graeco)
29. Macedonian Byzantine Catholic Church (Exarch is a Latin hierarch)
30. Russian (Byzantine) Greek-Catholic Church (Moscow) (currently, functioning under an Ordinariate, the hierarch of which is Latin))
31. Ruthenian (Byzantine) Greek-Catholic Church (Czech Republic)
Exarchial - Of Blessed Memory:
32. Georgian (Byzantine) Greek-Catholic Church (Exarchate of undetermined nature***)
33. Russian (Byzantine) Greek-Catholic Church (Harbin) (albeit, not yet formally acknowledged as extinct)
*Not of the same nature as the others but represents a unique instance of ordinary and personal jurisdiction and a not unique, but uncommon, instance of a metropolitanate erected with no suffragn jusridictions attached to it.
**In retrospect, by my exclusion of those jurisdictions outside the 'historical territories', I should not have included this one, as it is a diasporal jurisdiction (but I'm too lazy to remove it and renumber

)
***All of the other exarchates are Apostolic - created by and subject to Rome (and, therefore, not part and parcel of the standing canonical jurisdictions of the same Church, even where such exist).
It is unclear by whom the martyred Servant of God Father Exarch Shio (Batmalashvili) was designated as Exarch for the Georgian Byzantines. The most likely possibilities are the Servant of God Archbishop Andrej (Sheptytsky), Blessed Exarch Leonid (Feodorov), or Bishop Michel d'Herbigny.
If the latter, as d'Herbigny was functioning under Rome's authority, the office would have been deemed Apostolic; if either of the others, it would more likely have been deemed Archepiscopal/Episcopal. Father Exarch Shio himself was not elevated to the episcopate, as far as is known.
Many years,
Neil