Terminal command to enable / disable Stage Manager in the new System Settings in macOS Ventura

I am trying to write **an automation** using either Bash or AppleScript, **to enable / disable Stage Manager**, and this looks quite difficult to achieve. I cannot find much documentation around since in macOS Ventura the System Preferences have become System Settings, and there are not tabs anymore, so I ask whether anyone is able to achieve the task. It looks like I have found a possible answer here . However I have difficulties in pointing at the right Switch. Here is my script which does not work. It looks like I am having the groups messed up...

do shell script "open x-apple.systempreferences:com.apple.Desktop-Settings.extension"

tell application "System Events"
    tell its application process "System Settings"
        repeat until UI element 4 of group 1 of scroll area 1 of group 1 of ¬
          group 2 of splitter group 1 of group 1 of window "Desktop & Dock" exists
            delay 0.1
          end repeat
    		
          click checkbox "Stage Manager" of group 6 of scroll area 1 of group 1 of group 2 of splitter group 1 of group 1 of window "Desktop & Dock"
    end tell
end tell