Right now. WASM has been supported by every browser for a while now, and most webapps are made with WASM. That said, it’s not a replacement for Javascript, most people only use it on things that need to be high performance like heavier apps and web games. Nobody really makes websites that rely on WebAssembly instead of JS to my knowledge.
Also WASM can’t directly manipulate the DOM so it can’t really be used for handling HTML/CSS, all front-end stuff still has to be done with JS.