is it possible to split the content of the setting page. I would like to show the groups separately from settings (somewhere on the page via php) and of course the groups should be switched off on settings page. Is the possible?
It is possible but will require custom code. You will need to show groups and give users functionality to change their groups.
If you know php i can guide you, or you can hire any developer, Or you can contact us using https://www.shamimsplugins.com/hire/
Then show a form where you want your users can set their groups. You can get all groups using Fep_Group_Message::init()->get_all_groups() and user selected groups using Fep_Group_Message::init()->get_user_groups(). When they submit their form determine if they added or removed any group and save value accordingly.
You can get all in action in class-fep-group-message.php file. See this file.