All those go through JS as far as I'm aware. Emscripten bridges everything for you, but technically it goes through JS so SDL's calls also go through JS.
You're correct but I don't see why that matters. From your perspective as a C coder you get webgl access without having to write JS, that's what's important. Everything is "mixed together" into asm in the end anyway whether it's glue code in JS or browser side glue code.