There is no separate display server in Wayland. The window manager fulfils the roles that a display server would, using the libraries provided by the Wayland project.

Some of those are DE specific, especially the Gnome one,btw Gnome announced that they need to rewrite their code again it is wayland and X related so you should search and read that post if you missed it. I do not know all in the list but the Weston is a testing ground, not intended to be used as it is, some like Sway are full WM+compositor, Mate could not use it. I think it is a good idea to have a generic server that implements wayland, implements all the missing extension and all small DEs can use it if the user wants Wayland. Also Mir would continue to be used in IoT and other devices.