Homeschoolers form co-ops. A local one here does ballroom dance, tennis, basketball. There is often a youth symphony option in mid- to large-sized cities.

For STEM-type stuff, see if there's a nearby Civil Air Patrol squadron. That alone has tons of extracurricular stuff: search and rescue, help with earning a pilot license, robotics, drill and ceremony.

Homeschooling is not for everybody, but if you go down that route there's a lot of support.