I have a kid (10, developmentally younger). If money were no object, I would forgo kid school, hire a nanny to work 2pm-6pm weekdays, and ask her to sign him up for one cool class each of four days a week then take him to and from each. That would be my ideal.
In real life, I learned my son was very overstimulated by school, so I took him out, and then I learned that I was exhausted taking him to 4-6 community classes each week, so I stopped that too.
In our current circumstances, the optimal balance is that he's in 2-3 community classes or therapies per week, and in free play the rest of each day. (He voluntarily spends a couple of hours of his daily free play doing math, reading, science, etc.)
So, it just really depends: kid's age, capacity, temperament, as well as the caregiver's finances, energy levels, etc. But yeah, the kids show us when they're burning out in a day or week or month, and I propose we simply aim to have them in less than that. I don't really feel there's a formula beyond that, or indicators other than their level of joy, energy, and peace -and their chauffeur's. I can imagine that some kids would thrive in copious activities, in which case I would prioritize funding that. But I think for a lot of kids, especially those already in school all day, they are happier if we forgo excess.
My son is constantly being shorted opportunities -like, oh, school because our region forgot to support special needs kids- but I'm confident that if I focus on his joy, health, self-care, kindness, and relational abilities now, he will be able to pick up programming and algebra when things line up better for those.