I feel like we are going in circles, but I may have explained improperly or not understood correctly. The todoist app lets you check off tasks in the widget. The hue app lets you set scenes and control lights from the widget. They don’t open the app to complete those tasks. Another example is the widget for the shortcuts app. You can run shortcuts from the widget.
So, are those types of interactions possible from home screen widgets?
I was a bit confused before, I think there was a bit of a communication mishap but it could also well have been me.
Regardless, Shortcuts can still be run directly from the home screen widget, but the others, no.
Whether Shortcuts is "cheating" by being part of the OS, or it's because it can trigger it from a URI without opening the app I don't yet know.
It could still be possible to have some behaviour associated with widgets, but not something like ticking off a reminder. The native Reminders widget also no longer has that functionality.
While old-style widgets are still available, I am also sure that they will eventually be removed, though probably not before iOS 15.
Anything a widget is doing is encoded as a URI; essentially like a URL; URI being the more general format. So it would for example be possible to send the following URI when you tap a specific area in a widget:
todoist://deleteReminder/0?0
too trigger a function called deleteReminder on the 0th list of reminders and the 0th entry in there, but when iOS triggers the call, it will open the app to pass it the URI to handle.