Young Authors’ Workshop sounds like something your tween would like. They cover poetry, fiction, and nonfiction - read examples of the genres and then write their own. I think the best part is that they actually publish the campers writing and send the book to them at the end of camp. If your tween likes reading and writing I think they’d enjoy this camp.

Not sure of the age here, but NPS has a camp that goes up to grade 6 and does not have a specific emphasis on sports or music. The smaller groups could help an introverted kid make friendship connections, too.

There are a lot of options out there - Chess camp, STEM camp (but I'm thinking animation or worldbuilding or another story-telling based STEM topic), Drama Camp - I know you said introverted, but drama can be for introverts, too. For tweens, all camp experiences are better with a friend.

Writopia, if they are still in business w/ the pandemic

If so, any recommendations, for a somewhat introverted child who's into reading and writing?