So, uh... X11? VNC? RDP?

No no not something on top of the UI stack. They also need framebuffer support so they are big headache to setup on headless server.

What I mean is that we can bring some web tech to terminal natively. We don't even need a separated shell. Security and bi-directional communication is built by default because of UNIX socket. But we still need to think how to handle stuff like cookie, local storage, external CSS / JS, ...