He transfers his katra to McCoy, yet he's still fully functional, so his "soul" exists in two places at once.
Makes perfect sense. If I transfer a bit of software from my computer to yours, it is likely to remain fully functional in both. It would take very specific effort to remove it from my computer.
Then McCoy suddenly starts channeling Spock, apparently having all of Spock's knowledge and memories.
Hardly all. At most everything until the point of upload. And probably just the "essence", since this word was used by the Vulcans themselves to describe the katra business.
Then Spock's body gets regenerated and becomes a blank slate, but a blank slate that understands language and pon farr.
If it gets regenerated, it only makes sense that the katra in there gets regenerated as well. After all, a normal Vulcan child doesn't receive his katra from some outside source, as far as we know. It grows with him, from humble origins. The regenerated Spock's just would have some trouble growing apace with the body...
And we have no evidence that the regenerated Spock would have understood a word of any language until upgraded with the katra of a compatible adult (that is, the one from Spock's earlier, older self). Soothing sounds, yeah. Touch telepathy messages, perhaps. But not words.
Then the katra is rejoined, but suddenly has no memories or knowledge of pretty much anything, and whatever the hell was on the Genesis planet is apparently gone.
That makes the best sense of all. If Spock downloaded his life's story to McCoy in the engine room of the about-to-explode
Enterprise, then when McCoy dumps this back into Spock's noggin, that's where Spock's memories are likely to end: he'd remember next to nothing from between his death and his awakening after the mindswap. The adult katra is likely to overwrite the feeble contents of the at most week-old body's mind... It would be a much more demanding operation to somehow "intersplice" the two loads of data.
In any case, this sort of transferring of one's memories or "essence" doesn't look like a practical way to achieve eternal life or anything. It's not as if Surak would have remained alive in that jar in ENT: just some essential memories of him survived there. And it would probably not be a good idea to insert a dead celebrity's katra to a body that already possessed a naturally grown katra: the victim would probably go as mad as McCoy did. One would need very specific circumstances, a "more or less blank" receptor body, and probably a somehow "compatible" one to boot, and one would still only get a half-wit like the reborn Spock at best.
Timo Saloniemi