After tinkering with these some more, it seems that the ‘Large rectangle’ on the Modular and Infograph Modular faces does work, eventually. It’s a bit random, it took a few minutes to appear but it did finally change from the error message to the correct output. I didn’t change my template. Both {{states("alarm_control_panel.home_security")}} and {{states.alarm_control_panel.home_security.state}} seem to work equally sporadically.
I can’t get any other complication to work.
This is what the error message looked like:
After 5 or 10 minutes it eventually turned into this:
Some other complications seem to have their own issues 
:
