I think there are efforts within the WebAssembly GC to expose the DOM API directly to WASM programs.
I would assume this is the direction WASM is trying to go? It sounds so much cleaner, and it does seem the DOM being limited to JS is one of the showstoppers.
Yes, that's it and more. WASM is runtime idependent so it can run on cloud platforms or(in theory) even on bare metal interacting with the host through WASI