My kid worked every summer and did some sports stuff (not FT camp, maybe working out with his team a few evenings each week). Also vacationed a bit with us. Never any academic activities (beyond summer reading for the upcoming year.)
Your kid is getting plenty of academics during the year. Not sure why there would the need for more during the summer.
My kid got into selective (non-HYPS) schools with no hooks, good scores, and kinda middling plus grades with lots of rigor. Please don’t get flipped out by those posts.
And FWIW, I don’t think that AOs put much stock in any kind of “pay to play” opportunity. Your kid might get something out of it, but it’s unlikely to be an improved shot at admissions to an elite school. Your kid should be engaged somehow in s way that’sauthenticto her. Period. Don’t obsess too much over how.