With the operating system Raspbian GNU/Linux 12 (bookworm) it is possibile to choose between the traditional X11 graphical backend and the new Wayland. With X11 you can use only the Openbox window manager, while in Wayland you can choose Wayfire or the Labwc window manager.

Start the raspi-config and navigate the Advanced Options ⇒ Wayland to make your choice.

If you are using the default LightDM desktop manager, the settings are saved into /etc/lightdm/lightdm.conf. Here are the entries for Wayland Wayfire and Labwc respectively:

greeter-session=pi-greeter-wayfire
user-session=LXDE-pi-wayfire
autologin-session=LXDE-pi-wayfire
fallback-test=/usr/bin/xfallback.sh
fallback-session=LXDE-pi-x
fallback-greeter=pi-greeter

greeter-session=pi-greeter-labwc
user-session=LXDE-pi-labwc
autologin-session=LXDE-pi-labwc
#fallback-test=
#fallback-session=
#fallback-greeter=

From a terminal running in the graphical environment:

echo $XDG_SESSION_TYPE
x11

A more comprensive insight for a Wayland session:

set | grep XDG_SESSION
XDG_SESSION_CLASS=user
XDG_SESSION_DESKTOP=LXDE-pi-labwc
XDG_SESSION_ID=1
XDG_SESSION_PATH=/org/freedesktop/DisplayManager/Session0
XDG_SESSION_TYPE=wayland

First of all you have to stop the running graphical environment:

sudo systemctl stop lightdm.service

Then, as the unprivileged user, you can run the commad

wayfire-pi

or

labwc-pi

This can be useful to capture stdout and stderr messages from the window manager.