For best results, launch with Gamescope, so apps can launch inside of Steam. You may want to tweak the command line options depending of your setup.

/usr/share/wayland-sessions/steam-big-picture.desktop

[Desktop Entry]
Name=Steam Big Picture Mode
Comment=Start Steam in Big Picture Mode
Exec=/usr/bin/gamescope -e --expose-wayland --backend wayland --prefer-vk-device --disable-layers -- env WLR_RENDERER_ALLOW_SOFTWARE=1 steam -tenfoot -steamdeck
Type=Application

You can use drm or wayland for the backend option. Then you can configure SDDM to autostart Steam:

/etc/sddm.conf.d/autologin.conf

[Autologin]
User=yuki
Session=steam-big-picture

Works better if the above doesn't work. Also, lets you easily access the desktop without having to quit Steam. Start a desktop session (such as KDE), create an icon with this desktop file, add it to ~/.local/share/applications/, and link it in ~/.config/autostart/:

~/.local/share/applications/steam-big-picture.desktop

[Desktop Entry]
Name=Steam Big Picture Mode
Comment=Start Steam in Big Picture Mode
Exec=/usr/bin/env WLR_RENDERER_ALLOW_SOFTWARE=1 gamescope -e -W 1920 -H 1080 -f -g --expose-wayland --backend sdl -- /usr/bin/steam -tenfoot -steamdeck
Type=Application
Icon=steam

You can use sdl or wayland for the backend option. Don't forget SDDM's autologin:

/etc/sddm.conf.d/autologin.conf

[Autologin]
User=yuki
Session=plasma