In addition to SharedArrayBuffer, it looks like the atomics themselves are in-progress on Safari[1]. They don't work for me on Safari Technology Preview, FWIW.
As far as I can tell, “threads” from a WebAssembly implementation's perspective is just the combination of SharedArrayBuffer and atomics; support for the actual threading comes from Web Workers which are already a separate standard. Compilers like Emscripten then use the combination of the three to implement threading.