Provide twig variable, if the current logged in user is a group member

The way I implemented this is:

Create a function in a module that performs the checks you need (i.e. is user member of a group, has a role, etc).

function hook_preprocess_group(&$variables){
// do your logic checks here
$variables['group']->is_member = "yes";
}

By returning that logic check value to $variables['group'], it becomes available in your twig template: {{ group.is_member }}