It’s not the menu you need to adjust – it’s your roles and capabilities.
By default, a WP Core Author has “Dashboard” in their menu. You’re correct, they do not have a submenu under Dashboard, but clicking Dashboard takes them to the same page as “Dashboard > Home” for other users.
You may want to look through whatever plugins you’re using that may have adjusted permissions, and/or use a user role plugin to check what permissions users have. If they can’t see “Dashboard” at all, they need “read” capability added:
// hook to admin init
add_action('admin_init', 'add_author_caps');
function add_author_caps() {
// get the author role
$role = get_role('author');
// add "read" capability
$role->add_cap('read');
}
You can add this temporarily wherever you like – theme or plugin – and after you’ve logged in and viewed anything in wp-admin, you can remove this code as WP will save the capability.