I teach physics and a little calculus at a community college in California. My own kids went to local public high school, which is unusually good, and took the IB curriculum.
Sometimes in my physics classes, when discussing a topic like Newton's laws or DC circuits, I will use proof-based high school geometry as a reference point for the kind of formal reasoning and rigorous logic that is required. When I ask for a show of hands, about half my students say that they did two-column proofs in high school geometry. (This is usually accompanied with groans.)
My kids used a high school geometry textbook that did include a heavy dose of theorem proving, although proof was not emphasized as much as it would be if one was taking one's agenda directly from Euclid. To my taste, the approach was a little ugly and baroque, but the beautiful simplicity of Euclid was definitely embedded somewhere in there. The real number system was treated as something separate from but connected to geometry -- a strange and ugly approach, IMO.
I don't know if you're familiar with the US system. Our schools and curricula have traditionally been under completely local control, but over the last 40 years or so, control has gradually been shifting to the states and the federal government. We have something called Common Core, which is a set of national standards, which showed up around the same time that a well intended but sometimes farcical national political initiative called No Child Left Behind began to collapse under the weight of its impossible promises. Depressingly, Common Core says:
During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions and developing careful proofs. Later in college some students develop Euclidean and other geometries carefully from a small set of axioms.
If you try to parse this closely, it really doesn't make much sense. How does one do "careful proofs" without starting from "a small set of axioms?" It smells like language that was worked out as a compromise by a committee, taking into account the fact our educational system is neither able to provide rigorous educational opportunities for all, nor willing to make the attempt.