admin-bar-menu-filter.php

<?php
/**
 * Change site url in admin bar
 *
 * @param WP_Admin_Bar $wp_admin_bar
 */
function admin_bar_menu_filter( WP_Admin_Bar $wp_admin_bar ) {
	$new_url    = 'site.org';
	$site_name_node       = $wp_admin_bar->get_nodes()['site-name'];
	$site_name_node->href = $new_url;
	$view_site_node       = $wp_admin_bar->get_nodes()['view-site'];
	$view_site_node->href = $new_url;
	$wp_admin_bar->remove_node( 'site-name' );
	$wp_admin_bar->remove_node( 'view-site' );
	$wp_admin_bar->add_node( $site_name_node );
	$wp_admin_bar->add_node( $view_site_node );
}

add_filter( 'admin_bar_menu', 'admin_bar_menu_filter', 35 );

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