I wouldn't recommend using the generated classes for the button as this is randomly generated by a component we are using to add the styles of the button, JSS.
You are able to add a custom class by going to the group/button's advanced settings, under Custom ID & Custom Class.
Regarding the page blur, would you like the blur to happen after opening the group?
Because this might be possible with a custom script using our new API.
With our new API, you can run a custom script after a user has opened a group button. You can then make this script create a page blur. 🤔