A minor thing and I honestly wasn't on either side of this debate (wouldn't mind either way), but the new Live Letter does make confirmation that the bosses from Omega are not the same as those in FFV.

Q19. As an FFV fan, I was really excited to see how Omega: Deltascape was recreated. I’m really curious to find out if there’s any backstory for this. Could you please tell us anything?

A19. Thank you! In Final Fantasy V, Omega’s lore was set in a way where you didn’t know where it came from; therefore, people thought it came from the void. As for the bosses, they aren’t the same bosses from that game, but we did some trial and error to make them fit into FFXIV.

Also, there’s a rumor that there will be a V5.0, but there is no V5.0. We did mention that we’ll prepare a difficulty for those who complete Savage mode of V4.0; however, this isn’t V5.0.
Source

So despite taking place in the Dimensional Rift, which is where all the multiverse shenanigans in FF stem from, the lore is sticking to being self-contained (outside of seemingly non-canon crossover events).