This filter removes all unpublished posts and pages from WordPress menus.

wp-action-remove-draft-from-menu.php

<?php
add_filter( 'wp_nav_menu_objects', 'pst_nav_menu_objects', 10, 2 );

/**
 * Modify the WordPress menu and remove entries that are not visible for the current
 * user. This applies to all menus (primary, footer, widget ...)
 */
function pst_nav_menu_objects( $items, $args ) {
    // If you do not want to modify ALL menus, you can check for the menu-location 
    // or other criteria here.
    // For example, uncomment following condition to only modify the primary menu:
    # if ( 'primary' !== $args->theme_location ) {
    #     return $items;
    # }
    
    foreach ( $items as $key => $item ) {
        if ( ! in_array( $item->object, array( 'post', 'page' ) ) ) {
            // We only check visibility state for posts and pages.
            continue;
        }

        $post_status = get_post_status( $item->object_id );
        if ( 'publish' === $post_status ) {
            // This is a public page or post. No other check is needed.
            continue;
        }

        if ( is_user_logged_in() ) {
            if ( 'protected' === $post_status ) {
                if ( current_user_can( 'edit_post', $item->object_id ) ) {
                    // The current user is the author of the password protected post.
                    continue;
                }
            } else {
                if ( current_user_can( 'read_post', $item->object_id ) ) {
                    // The current user can read the draft or trashed post.
                    continue;
                }
            }
        }

        // All positive conditions failed.
        // Current visitor has no permission to see this menu entry.
        unset( $items[ $key ] );
    }

    return $items;
}