Unfortunately, lighting groups can only be controlled manually within the SmartThings app. They’re not even accessible in Scenes, Routines (Custom Automation), or other ‘first-party’ features from SmartThings.
I totally agree that it’s an odd choice. It’s like they implemented the base functionality and then just forgot about them.
I’ve seen some community members use rules to aggregate the status of devices into variables. You could then have a separate rule that you could run (using the hyperlink syntax) if you wanted a custom action to occur when the variable tile is tapped.