I agree that Rey responding to Palpatine either calling her nothing or a scavenger by stating she is a Jedi is the best thing, thematically. It’s the literal culmination of her character arcs - in TFA she hates being a lowly scavenger, in TLJ she hates that she’s a nobody in her own story. By the end of TROS, she has dealt with those things and become (in Joseph Campbell’s terms) the Master of Both Worlds, which in the SW universe has always meant being a Jedi.

Meanwhile, Palpatine being all the Sith is kind of irrelevant to anything meaningful across the trilogy.