WSL doesn't have an X Server, it has a Wayland compositor. That said, yes, you can use that. You can even run a different compositor nested so you get one single window with a desktop if you want.
Ah wayland. Many things changed since the time I've been using Linux in my professional work. However does Wayland support connectivity? I.e. can you display Wayland session on another computer via TCP/UDP? If not then Wayland won't work with wsl2 which is basically a VM
Not in the same way that X does. However, Microsoft specifically implemented an RDP backend into Weston, which ships with WSL2. So the Linux Windows you see are actually being sent over RDP transparently.
Seems very inefficient to have to render everything through the browser