Source

File: wp-admin/includes/class-wp-automatic-updater.php

protected function after_plugin_theme_update( $update_results ) {
		$successful_updates = array();
		$failed_updates     = array();

		/**
		 * Filters whether to send an email following an automatic background plugin update.
		 *
		 * @since 5.5.0
		 * @since 5.5.1 Added the $update_results parameter.
		 *
		 * @param bool  $enabled        True if plugins notifications are enabled, false otherwise.
		 * @param array $update_results The results of plugins update tasks.
		 */
		$notifications_enabled = apply_filters( 'auto_plugin_update_send_email', true, $update_results['plugin'] );

		if ( ! empty( $update_results['plugin'] ) && $notifications_enabled ) {
			foreach ( $update_results['plugin'] as $update_result ) {
				if ( true === $update_result->result ) {
					$successful_updates['plugin'][] = $update_result;
				} else {
					$failed_updates['plugin'][] = $update_result;
				}
			}
		}

		/**
		 * Filters whether to send an email following an automatic background theme update.
		 *
		 * @since 5.5.0
		 * @since 5.5.1 Added the $update_results parameter.
		 *
		 * @param bool  $enabled True if notifications are enabled, false otherwise.
		 * @param array $update_results The results of theme update tasks.
		 */
		$notifications_enabled = apply_filters( 'auto_theme_update_send_email', true, $update_results['theme'] );

		if ( ! empty( $update_results['theme'] ) && $notifications_enabled ) {
			foreach ( $update_results['theme'] as $update_result ) {
				if ( true === $update_result->result ) {
					$successful_updates['theme'][] = $update_result;
				} else {
					$failed_updates['theme'][] = $update_result;
				}
			}
		}

		if ( empty( $successful_updates ) && empty( $failed_updates ) ) {
			return;
		}

		if ( empty( $failed_updates ) ) {
			$this->send_plugin_theme_email( 'success', $successful_updates, $failed_updates );
		} elseif ( empty( $successful_updates ) ) {
			$this->send_plugin_theme_email( 'fail', $successful_updates, $failed_updates );
		} else {
			$this->send_plugin_theme_email( 'mixed', $successful_updates, $failed_updates );
		}
	}