How do I have WordPress use the tag for generated menus?

If you’re just trying to replace <ul...> and </ul> with <menu...> and </menu> in the generated HTML, you can use the wp_nav_menu filter:

add_filter( 'wp_nav_menu', 'wpse_426932_menu_fix' );
/**
 * Fixes the menu HTML to use <menu> instead of <ul>.
 *
 * @param  string $html The menu HTML.
 * @return string       The fixed menu HTML.
 */
function wpcs_426932_menu_fix( $html ) {
    $html = str_replace(
        array( '<ul', '</ul>' ),
        array( '<menu', '</menu>' ),
        $html
    );
    return $html;
}

You can add this code to your active theme’s functions.php file or you can make it into a simple plugin. (I tend to prefer the plugin route, because that way it keeps on working even if you change themes.)

Note: This is a very simple string replacement. If you need something more complex, you might need to use preg_replace().