I agree that Palpatine ‘pouring his power into Rey’ isn’t in Palpatine’s character, and is weird for the reasons you’ve enumerated here. So I’ve given it some more thought, and maybe we can use the whole ‘awakening’ angle from TFA to explain Rey’s power.
There is no hint of Rey’s power in the Force from an early age, so it could be assumed that she was chosen by the Force only when she truly needed it. Before this, she was just like any other person. Except that someone like Palpatine may have known that the Force was going to choose her and bestow in her great power, so if he knew this he would want to get to her first, and plant the seed of darkness in her. For this concept, she would need to stay on Jakku because that’s the only way she would be involved in the story and that’s how the Force eventually chooses her, so that means that Palpatine would want to keep her there on the planet until her awakening.
“I pushed you in the desert because I needed to see it…I needed you to see it…who you are. The dark side is your destiny. Rey…”
“You’re lying.”
“I’ve never lied to you. Your parents were no one. Junk traders from the outer rim.”
“Don’t!”
“They abandoned you for a reason. Don’t you know why?”
“I don’t want this!”
“It was Palpatine’s doing.”
“No!”
“He kept you on that planet.”
(Rey sees the vision of her parents and her abandonment.)
“My Love…be brave.”
“You’ll be safe here…I promise.”
“Come back! Nooo!”
“They were under duress. Forced to do the Emperor’s will.”
“Stop talking.”
“Rey…I know what happened to them.”
(Cutaway to heroes capture)
“Palpatine saw your future, Rey. So did I. A girl from nowhere, awakening to power. But you were there on Jakku because Palpatine wanted you there. And your parents played their part.”
(Rey sees her parents die.)
“She’s on Jakku; she’s gone.”
“No!”
“So that’s where you are.”
“You know why the Emperor always wanted you. I’ll come tell you.”
…
“Why did the Emperor come for me? Why did he want (to kill) a child? Tell me.”
“He saw what you would become. But before the Force chose you, you were chosen by Palpatine…to be his rightful heir.”
“You’re a Palpatine. Like my family, you are bound to him by a power greater than blood, a power like life itself. You can feel it…for it connects us as well. But we can destroy him, and bring a new order to the galaxy…together.”
“You know what you need to do. You know.”
“I do.”
…
If we focus on the connection between Rey and Kylo being like life itself, perhaps we can show that this connection, if it exists between Rey and Palpatine, supersedes any genetic connection or even manipulating midichlorians. The connection, the Force, is what’s important, far more than blood relationship.
This also recontextualizes Luke’s later statement about some things being stronger than blood, because here he’s taking it in a different direction and saying that found family or Rey’s commitment to the Jedi are stronger than her connection with Palpatine.
One thing that would need to be figured out with this direction is Finn’s dialogue later:
“He was going to Exegol with Ochi of Bestoon.”
“Why was Ochi going there?”
“To bring a little girl he was supposed to take from Jakku, to the Emperor.”
Changing it to:
“He went to Jakku with Ochi of Bestoon.”
“Why was Ochi going there?”
“To leave a little girl he was supposed to take from her parents, in the desert."