But if he was still clinging onto life through the offspring of the Skywalker’s, why would he even bother doing this with a random little girl, as well? She also cannot be called “a Palpatine” in this sequence of events.
Well we don’t know if he was just ‘clinging to life’ before TROS, just that he had returned at some point and was inhabiting a clone body.
My thought process on this is that Palpatine always wanted someone ‘far younger’ to inhabit, such as Anakin. He could have used the Force to create Anakin or not, but regardless, during ROTS he was probably looking to transfer his consciousness to him. Now, if life force transfer comes with visual changes in a person’s appearance, then we could easily see the moment when Palpatine went all-in with this plan - he used Windu’s attack as cover in order to mask the true cause of his transformation, while he transferred some of his power to Anakin. At this point, Anakin does almost a complete 180 and starts acting irredeemably evil. It was only Anakin’s fall on Mustafar that prevented Palpatine from going through with the full essence transfer, and it was probably Palpatine’s life force in Anakin that kept him alive.
Jumping forward to post-ROTJ, Palpatine probably reincarnated in a pristine clone body. Something after this transfer clearly happened to make this clone body deteriorate, and it may have been that he was transferring most of his life force into Rey in order that she could overcome her crises and be quickly drawn into the Dark Side. He probably planned to get her from Snoke during TFA or TLJ, but when Snoke failed he was forced to wait in a deteriorating clone body until Rey could find her way to him on her own.
The question still remains: Did Palpatine create Rey like he may have created Anakin? It could be that both Anakin and Rey had the Force from birth without Palpatine’s direct involvement, and he would only need to transfer some life force into them at the critical moments in order to corrupt them and their descendants. This seems to require the least effort on Palpatine’s part, and if Palpatine was able to survive his death due to his life force being bound within the Skywalkers, he would have been placed into a new clone body and so would have had the life force to begin this process again with Rey.
But why choose Rey? Perhaps among the Force sensitive candidates his cult could find at the time, she was the most powerful. Ben was doubtless heavily protected at this time, so Rey was the next best choice, a girl from nowhere whose parents wouldn’t be missed. He could have transferred his essence to her remotely, in which case her parents kept her from him, or in person, in which case he then sent her to Jakku to await her destiny.
In either case, the deterioration of Palpatine’s body seems to indicate that most of his power has been transferred to Rey by the time of TROS, and so she is essentially being devoured by Palpatine’s spirit. I’d argue that calling Rey a Palpatine here makes sense, and we could even keep it vague enough that she could have been created by Palpatine, it’s just another unknowable possibility.
And herein lies the main problem with the horcrux idea. It’s such a complex, hard-to-explain concept that it would take several minutes to properly explain it in a film format: minutes that we just don’t have. The hangar scene was only intended to convey a reveal as simple as “Palpatine is your granddad”, not lay out some deep saga lore.
If we want a reveal that we can seamlessly slot into a fanedit with almost no issues, then we need to keep it simple: most of the previous ideas in this thread did a pretty good job of this. But as it stands, I think the horcrux thing will be a dead end if we actually try to work it into the movie.