Arguably, couldn’t you say that in these instances that either a computer/technology or mind-meld is assembling a copy of their neurological pattern, and that copy is what is being transferred from place to place in the instances we’ve seen a person’s “consciousness” being put inside other bodies?
Not a “soul” per se. Think more like the “cookies” in Black Mirror (e.g., the digital copies of the employees in “USS Callister”).
To me, that fits better, since if Spock’s “soul” was put in McCoy before he goes into the chamber in Wrath of Khan, then who or what was talking to Kirk during his death? It makes more sense to think that a Katra is a “mental hard drive image” that’s been copied and the Spock we get back at the end of Search for Spock is not the original, but a copy of the original. I’d say the same thing for Picard at the end of season 1 of Picard.
On the flip side, there are Voyager episodes that imply the existence of a soul beyond consciousness transfer. Whatever that alien was that wanted to consume Janeway’s essence in death and spent an entire episode trying to convince her that he was her father and to accept death, seemed to imply there’s something beyond death and there’s a consciousness that goes somewhere else in death.