My two older kids never did any summer internships or academic programs, and both got into great colleges (one Ivy League, and one top 10 national university – neither with any legacy or other hook). My daughter went to camp in the summer (just regular camp-camp, nothing fancy). My son did some biking and wilderness type programs, but not designed to impress anyone, just because he likes hiking and camping, etc.
I think the reality is that no college admissions officer is impressed by the fancy-sounding internship that a high school kid gets because his uncle is friends with someone or whatever, and the job doesn’t really involve much more than watching what people are doing or stapling papers. As for academic programs, I think they could make a difference for a kid who goes to a significantly under-performing or rural public school and needs a way of showing academic interest/rigor. But for kids already going to challenging private schools, it really doesn’t add anything to the mix.