Continuing the discussion from Ventura Beta - detect status of Stage Manager:
I just [stumbled upon a way to enable/disable Stage Manager from the command line and it can be easily used to read the current state, I just don't know how to use as trigger.
To read the current state:
defaults read com.apple.WindowManager GloballyEnabled
And to turn it on or off:
defaults write com.apple.WindowManager GloballyEnabled -bool [true|false]
Sharing it in case it helps anyone.