Anything besides a cursory layperson's outlook on a lot of these topics (besides basic logic and history/philosophy of math -- although not sure how you would teach the last two/what you have in mind as curriculum) requires calculus and/or linear algebra. There is a reason they say you can never learn too much linear algebra.
And yes probability and statistics are fundamental. I was shocked a bit when I learned it was not taught in highschools world wide (i.e. not in the U.S.A.). But then again I had gotten numb with the current average level in the taught topics people arrive at undergrad at.
Note there is a lot of interconnectivity. To understand a new concept you might need concepts in another. E.g. number theory and probability.
In my experience, mathematics can be roughly divided in two: topics that use real numbers all the time, and topics that rarely need them. In the former, almost everything builds on calculus and/or linear algebra. In the latter, they are just two topics among many others.
The true foundational classes in the typical undergraduate mathematics curriculum are logic and abstract algebra. People rarely start with them, because the usual way of teaching mathematics is applications before foundations. You learn linear algebra before abstract algebra, proofs before formal logic, and axiomatic probability before measure theory.
And there is definitely such thing as too much linear algebra. Once upon a time, I wanted a decent mathematical background for theoretical CS and continued (at least) until the first graduate-level class in most major topics. Graduate linear algebra was "foundations without applications" for me, as I've never worked on anything building on it.
I think a layperson's outlook on these topics in high school could be very interesting though. Use this outlook to help motivate learning calculus and linear algebra. With a mix of engineering survey and math survey there are plenty of kids out there that would find parts of the course that stimulate their natural interest. Then the "calculus has many practical applications" thing would feel way less contrived. I mean of course I know now that it is true, but in high school I didn't feel it because I didn't have enough broader context.
A decade+ ago when I was in school, the policy was to push honors and AP classes for "college-bound" students. Stats (not offered as honors or AP in my school) was one of the fun courses that co-op kids got to take while we were stuck in pre-calc.
And yes probability and statistics are fundamental. I was shocked a bit when I learned it was not taught in highschools world wide (i.e. not in the U.S.A.). But then again I had gotten numb with the current average level in the taught topics people arrive at undergrad at.
Note there is a lot of interconnectivity. To understand a new concept you might need concepts in another. E.g. number theory and probability.