I know it's an old post, but I stumbled upon it googling for that exact question, so I figured, I'll point to a solution for anyone else in that situation. You CAN load vscode.dev in an iframe. In fact, you can load whatever you want in an iframe.

Now, I'm not saying it's trivial, just that it's doable. The trick would involve proxying it server-side. You'd have to find stategies to hide vscode.dev's context that it's running in an iframe.

(As a very inelegant PoC: the server could run it in a browser, send screenshots in a loop, listen for mouse and keyboard events and reproduce them in the browser running vscode.dev).