With all the vagueness of HOME and the move transfers, I choose to be pessimistic and interpret it as there not being any mixing of transfer moves between the Switch games. However this still leads to some different ways gamefreak can handle this depending on the interpretation of what learning a move entails, and if you can learn a move across games that you technically wouldn't have access to in one game alone. Here are some mysterious scenarios I propose. What answers do you think would happen?
1: Does Breloom learn Spore?
2: Can Hisuian Decidueye learn Astonish?
3: Can a non-hatched SV Pikachu learn Volt Tackle?
I have some updates to these minor mysteries now that I have access to HOME:
1: Breloom does not learn Spore. I haven't seen for myself, but it seems that the general consensus is that Breloom cannot carry Spore over from BDSP or any other game into SV. This also probably extends to 2: Decidueye and Astonish in the same way as being a move not listed in the actual learnset.
3: Despite the prior results, Pikachu does learn Volt Tackle! I transferred over a PLA native Raichu who was taught Volt Tackle and it kept it, so despite not being an egg move for the purposes of Mirror Herb, it is still recognized as part of Pikachu's learnset for the purposes of Home's memory and can be easily taught in PLA to any Pikachu family member.
I also taught Volt Tackle to the Flying Pikachu event and it worked the same way, so the combination of Fly and Volt Tackle is another moveset that's legalized now. The Unrivaled Pikachu can also gain Volt Tackle with no problem now.