WordPress Custom post type pagination not working

I am using Elementor child theme. I have created a custom post type " project ". I have showed 3 project per page. and I have create a pagination. But this pagination does not work if I don’t save " setting > reading > Blog pages show at most > 3 ". it’s showing me " The page can’t be found ". Althow I have 9 projects. But I don’t want to depend on this " setting > reading > Blog pages show at most ". because next time if I need to show 10 post per page, then it will difficult for me. So, now I want to show 3 projects per page. I can not find where I did wrong. Can anyone help me to solve this, please.

My next page permalink is this " .com/project/page/2/ ". but thi is not working. Only If I set the " setting > reading > Blog pages show at most > 3 " or low number then it’s working.

this is my code:

$paged = get_query_var('paged') ? get_query_var('paged') : 1;
                $args = array(
                    'post_type' => 'project',  // Custom post type name
                    'posts_per_page' => 3,         // Retrieve all posts
                    'paged'          => $paged,
                );
                $query = new WP_Query($args);
                if ($query->have_posts()) :

                    while ($query->have_posts()) : $query->the_post();
                        ?>
                        <div class="col-xl-4 col-md-6">
                            <a href="<?php the_permalink(); ?>" class="ad_project-item">
                                <?php the_post_thumbnail('full'); ?>
                                <h4><?php the_title(); ?></h4>
                            </a>
                        </div>
                    <?php
                    endwhile;

                    // Pagination
                    $big = 999999999; // need an unlikely integer
                    /*echo paginate_links(array(
                        'base'      => str_replace($big, '%#%', esc_url(get_pagenum_link($big))),
                        'format'    => '?paged=%#%',
                        'current'   => max(1, $paged),
                        'total'     => $query->max_num_pages
                    ));*/

                    $pagination = paginate_links(array(
                        'base' => str_replace($big, '%#%', get_pagenum_link($big)),
                        'format' => 'paged/%#%',
                        'current' => max(1, get_query_var('paged')),
                        'total' => $query->max_num_pages,
                        'prev_text' => __('&laquo; Previous'),
                        'next_text' => __('Next &raquo;'),
                        'type' => 'list',
                    ));
                    var_dump('Max num page :' . $query->max_num_pages);
                    if ($pagination) {
                        echo '<div class="pagination">' . $pagination . '</div>';
                    }

                    // Restore original post data
                    wp_reset_postdata();

                else :
                    echo '<p>No projects found.</p>';
                endif;
                ?>