Wayland is not a WM. https://wayland.freedesktop.org Wayland is the thing "underneath" a Window Manager. For example you can run KDE on top of X or Wayland. There are a few blurry boundaries in all this but that largely covers it.
No it doesn't. Wayland is the window server. [DWM](https://dwm.suckless.org) allows new windows to automatically be tiled when created. It also allows you also to change the way the tiling occurs when new windows are opened.
My new windows used to split an ever smaller portion of my screen in a fibonacci spiral based layout. I could also move between windows with hotkeys.
Rectangle is useful in a pinch, but it's no tiling window manager.