Lyxen
Great Old One
The literal functioning of the spell depends on whether you assume disappearing and and appearing to be two temporally distinct events, or merely the same event observed in different locations. I also don't think that figuring out the RAW is really that important. First off, there simply is not enough information and the rules are not written tightly enough that it would be possible to do so in this instance, and secondly, as Crawford is committed to demonstrating, literal RAW is often nonsensical mess.
Just to be clear, this is exactly my position as well, as expressed early in this post. I mostly try (but probably fail) to demonstrate that attempts at having only one explanation are usually wrong because the rules are written in an open fashion and in natural language, which leaves lots of room for interpretation.
In particular, if you want teleportation to be "unitary" in the sense that it cannot be split, I'm absolutely fine with it nothing says otherwise in the books. But neither do the books say that it is that way, other interpretations are just as valid, and I like to present them because sometimes, they lead to interesting possibilities in the game.
So just decide how you want it to work in your game, and do that. And inform the players of the ruling before they use the spell; the characters in the setting can be assumed to know how their magic works.
Indeed. And my further advice is to be benevolent towards your players, you are, after all, running this game for their fun. Having things blow up in their face just because one of the potential interpretations could be considered to say so is not really fun IMHO.