First, the tutor. Why is your son doing repetition with a tutor? That should be the one person who is teaching him at his pace and his level! I think that's an easy fix. Either the tutor changes approach or you change the tutor. It's OK if your son changes subject or jumps ahead. It's not a race. He should be able to explore topics to his heart's desire, regardless if he has the background. Usually, if you pursue a kids' interest, he will circle back and get the information he needs to fully understand the topic.
FWIW, I have a twin like yours.
Elementary school is hard to navigate. They just really aren't set up to deal with kids who are real outliers. We kept our boys together in elementary (in a gifted program), then in middle school, my PG twin just needed so much more than the school was willing to provide. So I pulled him out midway through 6th grade, homeschooled for 6 months until we found the right school, then skipped him into 8th. We also got him a math tutor who he has to this day (three years later). But they don't work on "school math." They explore other math concepts that are fun. It's not about having him accelerate through math-- it's about letting him see the beauty and fun of puzzling through difficult conceptual challenges. Maybe that's the angle you should pursue with your tutor, if your son's tutor is for math? Also, consider Beast Academy or Art of Problem Solving as his math program of he's old enough.My son says AoPS was the only thing that he looked forward to in 5th grade.
In the meantime, can you help him find ways to explore his passions at home?
I also tried really hard to make sure the boys had independent interests but also shared, joyful experiences so that they each had their own "thing," but they also had something that brought them together. They're not best friends now, but they like each other and enjoy spending time together.
Hang in there-- you'll figure it out.