From my understanding, it seems like what we want is a VNC switch in ssh rather than necessarilly display server specific functionality. Go even further and maybe the ssh server could just use the RFB protocol vnc uses.
Any Linux VNC server worth its salt already support tunneling RFB over ssh. To take it a step further, you would just need very little display server support for an ssh server to request the framebuffer of an application it opens and send it via RFB or the vnc server to the client.
And I'd imagine Wayland already has some mechanism for other applications to read somethings frames. If it is generic enough, ssh should be able to use that. My only concern is that Wayland would need to be rendering programs but not displaying them locally, and I don't have any understanding of Wayland's internal implementation enough to know if it supports hidden windows like that.