OldRiver

$wp_admin_bar->add_node() should be able to do what you want: https://codex.www.ads-software.com/Function_Reference/add_node

Specifically, you can take a look at this example from that page:

add_action( 'admin_bar_menu', 'toolbar_link_to_mypage', 999 );

function toolbar_link_to_mypage( $wp_admin_bar ) {
	$args = array(
		'id'    => 'my_page',
		'title' => 'My Page',
		'href'  => 'https://mysite.com/my-page/',
		'meta'  => array( 'class' => 'my-toolbar-page' )
	);
	$wp_admin_bar->add_node( $args );
}