Hide those annoying Automattic/WooCommerce/Jetpack/WordPress adverts & promos

functions.php

<?php
/**
 * Turn off WooCommerce Marketplace suggestions
 */
add_filter( 'woocommerce_allow_marketplace_suggestions', '__return_false' );

/**
 * Turn off WooCommerce Feature Plugin notice
 */
add_filter( 'woocommerce_show_admin_notice', '__return_false', 'wc_admin_feature_plugin_notice' );

/**
 * Turn off WooCommerce.com connection notice
 */
add_filter( 'woocommerce_helper_suppress_connect_notice', '__return_true' );

/**
 * Remove 'connect your store to WooCommerce.com' notice
 */
add_filter( 'woocommerce_helper_suppress_admin_notices', '__return_true' );

/**
 * Remove Jetpack Ads
 */
add_filter( 'jetpack_just_in_time_msgs', '__return_false' );

/**
 * Remove Site Health and PHP Dashboard Widgets
 */
function remove_site_wp_dashboard_widgets() {
	remove_meta_box( 'dashboard_site_health', 'dashboard', 'normal' );
	remove_meta_box( 'dashboard_php_nag', 'dashboard', 'normal' );
}
add_action( 'wp_dashboard_setup', 'remove_site_wp_dashboard_widgets' );