StreamDeck Toggle Button update state via script

I'm still trying to grasp all the unlimited possibilities and search around discussions and docs, so perhaps this is easy:

I want to use a StreamDeck Toggle On/Off Button to switch a HomeKit Scene, that works wonderful and easy e.g. via a Apple Shortcut.

However I want the state of the toggle button to be updated depending on the scene state.

What I tried so far:
Trigger Link
Copying the "Toggle On Action Sequence" trigger link runs the actions, but won't switch the state.
Copying the "Toggle On / Off Button" trigger link is like a button press, thus I can't set the state, but only toggle it.

Apple Script Widget with update_stream_deck_widget:
I know the right approach could e.g. be a Apple Script Widget and I know that I can

tell application "BetterTouchTool"
	update_stream_deck_widget "<uuid>" <stuff>

However I don't know how to figure out what would toggle the UUID toggle button state.

Any suggestions?