OPTION 1
In your template file, you could find the set content_classes and add another class name to the list.
{%
set content_classes = [
'class-name',
'class-name-other',
]
%}
<section{{ content_attributes.addClass(content_classes) }}>
OPTION 2
In your .theme file
function themename_preprocess_html(&$variables) {
$variables['content_attributes']['class'][] = 'class-name-other';
}
Note: This preprocess is for the html.html.twig file, you need to use the correct preprocess depending on your template file name.
If it's the node.html.twig then use function themename_preprocess_node(&$variables)
If it's the page.html.twig then use function themename_preprocess_page(&$variables)
