I'm only speculating, but the reason is likely because language servers are not written in JS. I assume electron apps can spin up arbitrary processes, allowing for a language servers to be written in anything. It'd be neat to see these language servers compiled to WASM and run as a web worker, although I suspect vscode isn't setup for that.

I think Codespaces is able to pull it off because the language servers, and vscode itself, is really running on Github's backends. They've set up the frontend to connect to a remote host.