> Right now wasm libs are limited in interop with JS and DOM. Could we have a .net/JVM like language-agnostic wasm standard lib bundled with all browsers, and target it like we do with .net standard?

There's already a plan to give WebAssembly direct access to DOM, and to any other API JavaScript would have access to, without needing a JavaScript shim. (This requires integration between WebAssembly and the JavaScript garbage collector, which is part of why it's taking time to develop.)