The shared memories they have through the dyad is definitely a sufficient explanation.

At this point, the only problem with this idea is that if Kylo really wanted to be finished with all of this, running away with Rey, then he definitely would have just killed Palpatine on Exegol. Because he wouldn’t care about being offered the fleet. There’s no reason he’d even hesitate killing him, and be curious by saying, “What could you give me?” Because this characterization is meant to emphasize that he doesn’t care about gaining power anymore.

One other thing worth noting is that his offer is technically a retread for Rey’s character from TFA, and one that is quite easy for her to accept this time around given the alternative. In that movie, Finn was the one asking her to just run away from all this with him. Now, yes, Kylo’s offer being to end the Sith is a retread of TLJ, but the difference would be the emphasis that she apparently belongs to Palpatine / is fated to be Palpatine’s. And that the only way to resist that would be to work together. Which makes her decision have a completely different context - join Kylo Ren to end the Sith and start a new dark order, or go alone and become the heir to the Sith. That’s an impossible decision to make.