This also likely varies, depending on the specific school.
My kids have attended different independent schools for middle school. One has had no costs in addition to tuition, other than a laptop. Anything done through the school was included in tuition, including books, school supplies, sports, music, field trips, extracurricular clubs, etc., including participating in competitions with entrance fees, etc. Literally no additional costs.
Another private middle school charged separately for each of those things, except books and school supplies - those were also included. Afterschool activities had additional fees. Competitions had additional fees. Field trips had additional fees. Those things, other than field trips, were all optional, I guess, so parents paid extra for their kids to participate in them.