Source

File: wp-admin/includes/class-wp-site-health-auto-updates.php

function test_check_wp_filesystem_method() {
		$skin    = new Automatic_Upgrader_Skin;
		$success = $skin->request_filesystem_credentials( false, ABSPATH );

		if ( ! $success ) {
			$description  = __( 'Your installation of WordPress prompts for FTP credentials to perform updates.' );
			$description .= ' ' . __( '(Your site is performing updates over FTP due to file ownership. Talk to your hosting company.)' );

			return array(
				'description' => $description,
				'severity'    => 'fail',
			);
		}

		return array(
			'description' => __( "Your installation of WordPress doesn't require FTP credentials to perform updates." ),
			'severity'    => 'pass',
		);
	}